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  Subjects -> MATHEMATICS (Total: 879 journals)
    - APPLIED MATHEMATICS (71 journals)
    - GEOMETRY AND TOPOLOGY (19 journals)
    - MATHEMATICS (651 journals)
    - MATHEMATICS (GENERAL) (42 journals)
    - NUMERICAL ANALYSIS (19 journals)
    - PROBABILITIES AND MATH STATISTICS (77 journals)

MATHEMATICS (651 journals)                  1 2 3 4 | Last

Showing 1 - 200 of 538 Journals sorted alphabetically
Abakós     Open Access   (Followers: 3)
Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg     Hybrid Journal   (Followers: 2)
Academic Voices : A Multidisciplinary Journal     Open Access   (Followers: 2)
Accounting Perspectives     Full-text available via subscription   (Followers: 8)
ACM Transactions on Algorithms (TALG)     Hybrid Journal   (Followers: 16)
ACM Transactions on Computational Logic (TOCL)     Hybrid Journal   (Followers: 4)
ACM Transactions on Mathematical Software (TOMS)     Hybrid Journal   (Followers: 6)
ACS Applied Materials & Interfaces     Full-text available via subscription   (Followers: 21)
Acta Applicandae Mathematicae     Hybrid Journal   (Followers: 1)
Acta Mathematica     Hybrid Journal   (Followers: 11)
Acta Mathematica Hungarica     Hybrid Journal   (Followers: 2)
Acta Mathematica Scientia     Full-text available via subscription   (Followers: 5)
Acta Mathematica Sinica, English Series     Hybrid Journal   (Followers: 5)
Acta Mathematica Vietnamica     Hybrid Journal  
Acta Mathematicae Applicatae Sinica, English Series     Hybrid Journal  
Advanced Science Letters     Full-text available via subscription   (Followers: 7)
Advances in Applied Clifford Algebras     Hybrid Journal   (Followers: 3)
Advances in Calculus of Variations     Hybrid Journal   (Followers: 2)
Advances in Catalysis     Full-text available via subscription   (Followers: 5)
Advances in Complex Systems     Hybrid Journal   (Followers: 7)
Advances in Computational Mathematics     Hybrid Journal   (Followers: 15)
Advances in Decision Sciences     Open Access   (Followers: 4)
Advances in Difference Equations     Open Access   (Followers: 1)
Advances in Fixed Point Theory     Open Access   (Followers: 5)
Advances in Geosciences (ADGEO)     Open Access   (Followers: 10)
Advances in Linear Algebra & Matrix Theory     Open Access   (Followers: 1)
Advances in Materials Sciences     Open Access   (Followers: 16)
Advances in Mathematical Physics     Open Access   (Followers: 5)
Advances in Mathematics     Full-text available via subscription   (Followers: 10)
Advances in Numerical Analysis     Open Access   (Followers: 4)
Advances in Operations Research     Open Access   (Followers: 11)
Advances in Porous Media     Full-text available via subscription   (Followers: 4)
Advances in Pure and Applied Mathematics     Hybrid Journal   (Followers: 5)
Advances in Pure Mathematics     Open Access   (Followers: 4)
Advances in Science and Research (ASR)     Open Access   (Followers: 6)
Aequationes Mathematicae     Hybrid Journal   (Followers: 2)
African Journal of Educational Studies in Mathematics and Sciences     Full-text available via subscription   (Followers: 5)
African Journal of Mathematics and Computer Science Research     Open Access   (Followers: 4)
Afrika Matematika     Hybrid Journal   (Followers: 1)
Air, Soil & Water Research     Open Access   (Followers: 7)
AKSIOMA Journal of Mathematics Education     Open Access   (Followers: 1)
Algebra and Logic     Hybrid Journal   (Followers: 3)
Algebra Colloquium     Hybrid Journal   (Followers: 4)
Algebra Universalis     Hybrid Journal   (Followers: 2)
Algorithmic Operations Research     Full-text available via subscription   (Followers: 5)
Algorithms     Open Access   (Followers: 10)
Algorithms Research     Open Access   (Followers: 1)
American Journal of Biostatistics     Open Access   (Followers: 9)
American Journal of Computational and Applied Mathematics     Open Access   (Followers: 3)
American Journal of Mathematical Analysis     Open Access  
American Journal of Mathematics     Full-text available via subscription   (Followers: 7)
American Journal of Operations Research     Open Access   (Followers: 5)
American Mathematical Monthly     Full-text available via subscription   (Followers: 6)
An International Journal of Optimization and Control: Theories & Applications     Open Access   (Followers: 7)
Analele Universitatii Ovidius Constanta - Seria Matematica     Open Access   (Followers: 1)
Analysis     Hybrid Journal   (Followers: 2)
Analysis and Applications     Hybrid Journal   (Followers: 1)
Analysis and Mathematical Physics     Hybrid Journal   (Followers: 3)
Analysis Mathematica     Full-text available via subscription  
Annales Mathematicae Silesianae     Open Access  
Annales mathématiques du Québec     Hybrid Journal   (Followers: 4)
Annales UMCS, Mathematica     Open Access   (Followers: 1)
Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica     Open Access  
Annali di Matematica Pura ed Applicata     Hybrid Journal   (Followers: 1)
Annals of Combinatorics     Hybrid Journal   (Followers: 3)
Annals of Data Science     Hybrid Journal   (Followers: 8)
Annals of Discrete Mathematics     Full-text available via subscription   (Followers: 6)
Annals of Mathematics     Full-text available via subscription  
Annals of Mathematics and Artificial Intelligence     Hybrid Journal   (Followers: 6)
Annals of Pure and Applied Logic     Open Access   (Followers: 2)
Annals of the Alexandru Ioan Cuza University - Mathematics     Open Access  
Annals of the Institute of Statistical Mathematics     Hybrid Journal   (Followers: 1)
Annals of West University of Timisoara - Mathematics     Open Access  
Annuaire du Collège de France     Open Access   (Followers: 5)
Applicable Algebra in Engineering, Communication and Computing     Hybrid Journal   (Followers: 2)
Applications of Mathematics     Hybrid Journal   (Followers: 1)
Applied Categorical Structures     Hybrid Journal   (Followers: 2)
Applied Computational Intelligence and Soft Computing     Open Access   (Followers: 12)
Applied Mathematics     Open Access   (Followers: 3)
Applied Mathematics     Open Access   (Followers: 4)
Applied Mathematics & Optimization     Hybrid Journal   (Followers: 4)
Applied Mathematics - A Journal of Chinese Universities     Hybrid Journal  
Applied Mathematics Letters     Full-text available via subscription   (Followers: 1)
Applied Mathematics Research eXpress     Hybrid Journal   (Followers: 1)
Applied Network Science     Open Access  
Applied Numerical Mathematics     Hybrid Journal   (Followers: 5)
Applied Spatial Analysis and Policy     Hybrid Journal   (Followers: 4)
Arab Journal of Mathematical Sciences     Open Access   (Followers: 2)
Arabian Journal of Mathematics     Open Access   (Followers: 2)
Archive for Mathematical Logic     Hybrid Journal   (Followers: 1)
Archive of Applied Mechanics     Hybrid Journal   (Followers: 4)
Archive of Numerical Software     Open Access  
Archives of Computational Methods in Engineering     Hybrid Journal   (Followers: 4)
Arkiv för Matematik     Hybrid Journal   (Followers: 1)
Arnold Mathematical Journal     Hybrid Journal   (Followers: 1)
Artificial Satellites : The Journal of Space Research Centre of Polish Academy of Sciences     Open Access   (Followers: 19)
Asia-Pacific Journal of Operational Research     Hybrid Journal   (Followers: 3)
Asian Journal of Algebra     Open Access   (Followers: 1)
Asian Journal of Current Engineering & Maths     Open Access  
Asian-European Journal of Mathematics     Hybrid Journal   (Followers: 2)
Australian Mathematics Teacher, The     Full-text available via subscription   (Followers: 7)
Australian Primary Mathematics Classroom     Full-text available via subscription   (Followers: 2)
Australian Senior Mathematics Journal     Full-text available via subscription   (Followers: 1)
Automatic Documentation and Mathematical Linguistics     Hybrid Journal   (Followers: 5)
Axioms     Open Access  
Baltic International Yearbook of Cognition, Logic and Communication     Open Access  
Basin Research     Hybrid Journal   (Followers: 3)
BIBECHANA     Open Access  
BIT Numerical Mathematics     Hybrid Journal  
BoEM - Boletim online de Educação Matemática     Open Access  
Boletim Cearense de Educação e História da Matemática     Open Access  
Boletim de Educação Matemática     Open Access  
Boletín de la Sociedad Matemática Mexicana     Hybrid Journal  
Bollettino dell'Unione Matematica Italiana     Full-text available via subscription   (Followers: 1)
British Journal of Mathematical and Statistical Psychology     Full-text available via subscription   (Followers: 21)
Bruno Pini Mathematical Analysis Seminar     Open Access  
Buletinul Academiei de Stiinte a Republicii Moldova. Matematica     Open Access   (Followers: 7)
Bulletin des Sciences Mathamatiques     Full-text available via subscription   (Followers: 4)
Bulletin of Dnipropetrovsk University. Series : Communications in Mathematical Modeling and Differential Equations Theory     Open Access   (Followers: 1)
Bulletin of Mathematical Sciences     Open Access   (Followers: 1)
Bulletin of the Brazilian Mathematical Society, New Series     Hybrid Journal  
Bulletin of the London Mathematical Society     Hybrid Journal   (Followers: 3)
Bulletin of the Malaysian Mathematical Sciences Society     Hybrid Journal  
Calculus of Variations and Partial Differential Equations     Hybrid Journal  
Canadian Journal of Science, Mathematics and Technology Education     Hybrid Journal   (Followers: 18)
Carpathian Mathematical Publications     Open Access   (Followers: 1)
Catalysis in Industry     Hybrid Journal   (Followers: 1)
CEAS Space Journal     Hybrid Journal  
CHANCE     Hybrid Journal   (Followers: 5)
Chaos, Solitons & Fractals     Hybrid Journal   (Followers: 3)
ChemSusChem     Hybrid Journal   (Followers: 7)
Chinese Annals of Mathematics, Series B     Hybrid Journal  
Chinese Journal of Catalysis     Full-text available via subscription   (Followers: 2)
Chinese Journal of Mathematics     Open Access  
Clean Air Journal     Full-text available via subscription   (Followers: 2)
Cogent Mathematics     Open Access   (Followers: 2)
Cognitive Computation     Hybrid Journal   (Followers: 4)
Collectanea Mathematica     Hybrid Journal  
College Mathematics Journal     Full-text available via subscription   (Followers: 2)
COMBINATORICA     Hybrid Journal  
Combustion Theory and Modelling     Hybrid Journal   (Followers: 13)
Commentarii Mathematici Helvetici     Hybrid Journal   (Followers: 1)
Communications in Contemporary Mathematics     Hybrid Journal  
Communications in Mathematical Physics     Hybrid Journal   (Followers: 1)
Communications On Pure & Applied Mathematics     Hybrid Journal   (Followers: 3)
Complex Analysis and its Synergies     Open Access   (Followers: 2)
Complex Variables and Elliptic Equations: An International Journal     Hybrid Journal  
Complexus     Full-text available via subscription  
Composite Materials Series     Full-text available via subscription   (Followers: 9)
Comptes Rendus Mathematique     Full-text available via subscription   (Followers: 1)
Computational and Applied Mathematics     Hybrid Journal   (Followers: 2)
Computational and Mathematical Methods in Medicine     Open Access   (Followers: 2)
Computational and Mathematical Organization Theory     Hybrid Journal   (Followers: 2)
Computational Complexity     Hybrid Journal   (Followers: 4)
Computational Mathematics and Modeling     Hybrid Journal   (Followers: 8)
Computational Mechanics     Hybrid Journal   (Followers: 4)
Computational Methods and Function Theory     Hybrid Journal  
Computational Optimization and Applications     Hybrid Journal   (Followers: 7)
Computers & Mathematics with Applications     Full-text available via subscription   (Followers: 5)
Concrete Operators     Open Access   (Followers: 4)
Confluentes Mathematici     Hybrid Journal  
COSMOS     Hybrid Journal  
Cryptography and Communications     Hybrid Journal   (Followers: 14)
Cuadernos de Investigación y Formación en Educación Matemática     Open Access  
Cubo. A Mathematical Journal     Open Access  
Czechoslovak Mathematical Journal     Hybrid Journal   (Followers: 1)
Demographic Research     Open Access   (Followers: 11)
Demonstratio Mathematica     Open Access  
Dependence Modeling     Open Access  
Design Journal : An International Journal for All Aspects of Design     Hybrid Journal   (Followers: 29)
Developments in Clay Science     Full-text available via subscription   (Followers: 1)
Developments in Mineral Processing     Full-text available via subscription   (Followers: 3)
Dhaka University Journal of Science     Open Access  
Differential Equations and Dynamical Systems     Hybrid Journal   (Followers: 2)
Discrete Mathematics     Hybrid Journal   (Followers: 7)
Discrete Mathematics & Theoretical Computer Science     Open Access  
Discrete Mathematics, Algorithms and Applications     Hybrid Journal   (Followers: 2)
Discussiones Mathematicae Graph Theory     Open Access   (Followers: 1)
Doklady Mathematics     Hybrid Journal  
Duke Mathematical Journal     Full-text available via subscription   (Followers: 1)
Edited Series on Advances in Nonlinear Science and Complexity     Full-text available via subscription  
Electronic Journal of Graph Theory and Applications     Open Access   (Followers: 2)
Electronic Notes in Discrete Mathematics     Full-text available via subscription   (Followers: 2)
Elemente der Mathematik     Full-text available via subscription   (Followers: 3)
Energy for Sustainable Development     Hybrid Journal   (Followers: 9)
Enseñanza de las Ciencias : Revista de Investigación y Experiencias Didácticas     Open Access  
Ensino da Matemática em Debate     Open Access  
Entropy     Open Access   (Followers: 5)
ESAIM: Control Optimisation and Calculus of Variations     Full-text available via subscription   (Followers: 1)
European Journal of Combinatorics     Full-text available via subscription   (Followers: 4)
European Journal of Mathematics     Hybrid Journal   (Followers: 1)
European Scientific Journal     Open Access   (Followers: 2)
Experimental Mathematics     Hybrid Journal   (Followers: 4)
Expositiones Mathematicae     Hybrid Journal   (Followers: 2)
Facta Universitatis, Series : Mathematics and Informatics     Open Access  
Fasciculi Mathematici     Open Access  
Finite Fields and Their Applications     Full-text available via subscription   (Followers: 4)
Fixed Point Theory and Applications     Open Access   (Followers: 1)
Formalized Mathematics     Open Access   (Followers: 2)
Foundations and Trends® in Econometrics     Full-text available via subscription   (Followers: 4)

        1 2 3 4 | Last

Journal Cover Applied Mathematics Letters
  [SJR: 1.141]   [H-I: 65]   [1 followers]  Follow
    
   Full-text available via subscription Subscription journal
   ISSN (Print) 0893-9659
   Published by Elsevier Homepage  [3042 journals]
  • Attractivity for fractional differential equations in Banach space
    • Authors: Yong Zhou
      Pages: 1 - 6
      Abstract: Publication date: January 2018
      Source:Applied Mathematics Letters, Volume 75
      Author(s): Yong Zhou
      In this paper, we initiate the question of attractivity of solutions for fractional differential equations in abstract space. We establish sufficient conditions for the existence of globally attractive solutions for the Cauchy problems. Our results essentially reveal the characteristics of solutions for fractional differential equations with the Riemann–Liouville derivative.

      PubDate: 2017-07-12T02:41:55Z
      DOI: 10.1016/j.aml.2017.06.008
      Issue No: Vol. 75 (2017)
       
  • Local super-quadratic conditions on homoclinic solutions for a
           second-order Hamiltonian system
    • Authors: Xiaoping Wang
      Pages: 7 - 12
      Abstract: Publication date: January 2018
      Source:Applied Mathematics Letters, Volume 75
      Author(s): Xiaoping Wang
      In this paper, we study the homoclinic solutions of the following second-order Hamiltonian system u ̈ − L ( t ) u + ∇ W ( t , u ) = 0 , where t ∈ R , u ∈ R N , L : R → R N × N and W : R × R N → R . Applying the Mountain Pass Theorem, we prove the existence of nontrivial homoclinic solutions under new weaker conditions. In particular, we use a local super-quadratic condition lim x → ∞ W ( t , x ) x 2 = ∞ , uniformly in t ∈ ( a , b ) for some − ∞ < a < b < + ∞ , instead of the common one lim x → ∞ W ( t , x ) x 2 = ∞ , uniformly in t ∈ R , which is essential to show the existence of nontrivial homoclinic solutions for the above system in all existing literature.

      PubDate: 2017-07-12T02:41:55Z
      DOI: 10.1016/j.aml.2017.06.009
      Issue No: Vol. 75 (2017)
       
  • Inverse problems for second order integro-differential operators
    • Authors: Vjacheslav Yurko
      Pages: 1 - 6
      Abstract: Publication date: December 2017
      Source:Applied Mathematics Letters, Volume 74
      Author(s): Vjacheslav Yurko
      Inverse spectral problems are studied for the first order integro-differential operators on a finite interval. Properties of spectral characteristic are established, and a constructive algorithm is provided for this class of inverse problems.

      PubDate: 2017-06-06T15:00:28Z
      DOI: 10.1016/j.aml.2017.04.013
      Issue No: Vol. 74 (2017)
       
  • Exact solutions for a coupled discrete nonlinear Schrödinger system with
           a saturation nonlinearity
    • Authors: Qing Zhu; Zhan Zhou; Lin Wang
      Pages: 7 - 14
      Abstract: Publication date: December 2017
      Source:Applied Mathematics Letters, Volume 74
      Author(s): Qing Zhu, Zhan Zhou, Lin Wang
      Deriving exact solutions of nonlinear evolution equations has recently received tremendous attention in mathematics and physics. In this paper, using the ( G ′ ∕ G ) -expansion method, we obtain some exact solutions for a coupled discrete nonlinear Schrödinger system with a saturation nonlinearity. These exact solutions include the hyperbolic function type, trigonometric function type and rational function type, of which the hyperbolic function type solutions may generate kink and anti-kink solitons.

      PubDate: 2017-06-06T15:00:28Z
      DOI: 10.1016/j.aml.2017.05.003
      Issue No: Vol. 74 (2017)
       
  • Blowup for the solutions of the Euler–Poisson equations with damping
    • Authors: Jianli Liu; Yaoli Fang
      Pages: 15 - 19
      Abstract: Publication date: December 2017
      Source:Applied Mathematics Letters, Volume 74
      Author(s): Jianli Liu, Yaoli Fang
      In this short paper, we consider the formation of singularities for the solutions of the Euler–Poisson equations with damping with attractive forces in R n ( n ≥ 1 ) and the repulsive forces in R . Under the appropriate assumptions on initial data, we can obtain the divergence of the velocity will blowup in the finite time.

      PubDate: 2017-06-06T15:00:28Z
      DOI: 10.1016/j.aml.2017.05.008
      Issue No: Vol. 74 (2017)
       
  • Non-Nehari manifold method for a class of generalized quasilinear
           Schrödinger equations
    • Authors: Jianhua Chen; Xianhua Tang; Bitao Cheng
      Pages: 20 - 26
      Abstract: Publication date: December 2017
      Source:Applied Mathematics Letters, Volume 74
      Author(s): Jianhua Chen, Xianhua Tang, Bitao Cheng
      In this paper, we study the following generalized quasilinear Schrödinger equation − d i v ( g 2 ( u ) ∇ u ) + g ( u ) g ′ ( u ) ∇ u 2 + V ( x ) u = f ( x , u ) , x ∈ R N , where N ≥ 3 , 2 ∗ = 2 N N − 2 , g ∈ C 1 ( R , R + ) , V ( x ) and f ( x , u ) are 1-periodic on x . By using a change of variable, we obtain the existence of ground states solutions. Unlike the Nahari manifold method, the main idea of our approach lies on finding a minimizing Cerami sequence for the energy functional outside the manifold by using the diagonal method.

      PubDate: 2017-06-11T15:09:32Z
      DOI: 10.1016/j.aml.2017.04.032
      Issue No: Vol. 74 (2017)
       
  • Invasion speed of a predator–prey system
    • Authors: Shuxia Pan
      Pages: 46 - 51
      Abstract: Publication date: December 2017
      Source:Applied Mathematics Letters, Volume 74
      Author(s): Shuxia Pan
      This paper is concerned with the asymptotic spreading of a predator–prey system, which formulates that the predator invades the habitat of the prey. By constructing auxiliary equation, we obtain the speed of asymptotic spreading of the predator.

      PubDate: 2017-06-11T15:09:32Z
      DOI: 10.1016/j.aml.2017.05.014
      Issue No: Vol. 74 (2017)
       
  • Existence and uniqueness of normalized solutions for the Kirchhoff
           equation
    • Authors: Xiaoyu Zeng; Yimin Zhang
      Pages: 52 - 59
      Abstract: Publication date: December 2017
      Source:Applied Mathematics Letters, Volume 74
      Author(s): Xiaoyu Zeng, Yimin Zhang
      For a class of Kirchhoff functional, we first give a complete classification with respect to the exponent p for its L 2 -normalized critical points, and show that the minimizer of the functional, if exists, is unique up to translations. Secondly, we search for the mountain pass type critical points for the functional on the L 2 -normalized manifold, and also prove that this type critical point is unique up to translations. Our proof relies only on some simple energy estimates and avoids using the concentration-compactness principles. These conclusions extend some known results in previous papers.

      PubDate: 2017-06-11T15:09:32Z
      DOI: 10.1016/j.aml.2017.05.012
      Issue No: Vol. 74 (2017)
       
  • On the uniqueness of solutions for a class of fractional differential
           equations
    • Authors: Yumei Zou; Guoping He
      Pages: 68 - 73
      Abstract: Publication date: December 2017
      Source:Applied Mathematics Letters, Volume 74
      Author(s): Yumei Zou, Guoping He
      We are concerned with the uniqueness of solutions for the following nonlinear fractional boundary value problem: D p x ( t ) + f ( t , x ( t ) ) = 0 , 2 < p ≤ 3 , t ∈ ( 0 , 1 ) , x ( 0 ) = x ′ ( 0 ) = 0 , x ( 1 ) = 0 where D 0 + p denotes the standard Riemann–Liouville fractional derivative. Our analysis relies on the theory of linear operators and the ‖ ⋅ ‖ e norm.

      PubDate: 2017-06-11T15:09:32Z
      DOI: 10.1016/j.aml.2017.05.011
      Issue No: Vol. 74 (2017)
       
  • A note on a family of non-gravitational central force potentials in
           dimension one
    • Authors: M. Alvarez-Ramírez; M. Corbera; Josep M. Cors; A. García
      Pages: 74 - 78
      Abstract: Publication date: December 2017
      Source:Applied Mathematics Letters, Volume 74
      Author(s): M. Alvarez-Ramírez, M. Corbera, Josep M. Cors, A. García
      In this work, we study a one-parameter family of differential equations and the different scenarios that arise with the change of parameter. We remark that these are not bifurcations in the usual sense but a wider phenomenon related with changes of continuity or differentiability. We offer an alternative point of view for the study for the motion of a system of two particles which will always move in some fixed line, we take R for the position space. If we fix the center of mass at the origin, the system reduces to that of a single particle of unit mass in a central force field. We take the potential energy function U ( x ) = x β , where x is the position of the single particle and β is some positive real number.

      PubDate: 2017-06-11T15:09:32Z
      DOI: 10.1016/j.aml.2017.04.020
      Issue No: Vol. 74 (2017)
       
  • Uniform local well-posedness for an Ericksen–Leslie’s
           density-dependent parabolic–hyperbolic liquid crystals model
    • Authors: Jishan Fan; Yong Zhou
      Pages: 79 - 84
      Abstract: Publication date: December 2017
      Source:Applied Mathematics Letters, Volume 74
      Author(s): Jishan Fan, Yong Zhou
      We prove uniform local-in-time existence and uniqueness of solutions to an Ericksen–Leslie’s density-dependent parabolic–hyperbolic liquid crystals model.

      PubDate: 2017-06-11T15:09:32Z
      DOI: 10.1016/j.aml.2017.04.012
      Issue No: Vol. 74 (2017)
       
  • Entire blow-up solutions for a quasilinear p-Laplacian Schrödinger
           equation with a non-square diffusion term
    • Authors: Xinguang Zhang; Lishan Liu; Yonghong Wu; Yujun Cui
      Pages: 85 - 93
      Abstract: Publication date: December 2017
      Source:Applied Mathematics Letters, Volume 74
      Author(s): Xinguang Zhang, Lishan Liu, Yonghong Wu, Yujun Cui
      In this paper, we study the entire blow-up solutions for a quasilinear p -Laplacian Schrödinger elliptic equation with a non-square diffusion term. By using the dual approach and some new iterative techniques, the difficulty due to the non-square diffusion term and the p -Laplacian operator is overcome and the nonexistence and existence of entire blow-up solutions are established.

      PubDate: 2017-06-16T15:31:56Z
      DOI: 10.1016/j.aml.2017.05.010
      Issue No: Vol. 74 (2017)
       
  • On a high-order one-parameter family for the simultaneous determination of
           polynomial roots
    • Authors: L.D. Petković; M.S. Petković
      Pages: 94 - 101
      Abstract: Publication date: December 2017
      Source:Applied Mathematics Letters, Volume 74
      Author(s): L.D. Petković, M.S. Petković
      A new one-parameter family of simultaneous methods for the determination of all (simple or multiple) zeros of a polynomial is derived. The order of the basic family of simultaneous methods is four. Using suitable corrective approximations, the order of convergence of this family is increased even to six without any additional evaluations of the polynomial and its derivatives, which points to a high computational efficiency of the new family of root solvers. Comparison with the existing methods in regard to computational efficiency and numerical examples are also performed.

      PubDate: 2017-06-16T15:31:56Z
      DOI: 10.1016/j.aml.2017.05.013
      Issue No: Vol. 74 (2017)
       
  • Blow-up of solutions to the Patlak–Keller–Segel equation in
           dimension ν≥2
    • Authors: Li Chen; Heinz Siedentop
      Pages: 102 - 107
      Abstract: Publication date: December 2017
      Source:Applied Mathematics Letters, Volume 74
      Author(s): Li Chen, Heinz Siedentop
      We prove a blow-up criterion for the solutions to the ν -dimensional Patlak–Keller–Segel equation in the whole space. The condition is new in dimension three and higher. In dimension two, it is exactly Dolbeault’s and Perthame’s blow-up condition, i.e., blow-up occurs, if the total mass exceeds 8 π .

      PubDate: 2017-06-16T15:31:56Z
      DOI: 10.1016/j.aml.2017.05.006
      Issue No: Vol. 74 (2017)
       
  • Remarks on Bernoulli constants, gauge conditions and phase velocities in
           the context of water waves
    • Authors: Didier Clamond
      Pages: 114 - 120
      Abstract: Publication date: December 2017
      Source:Applied Mathematics Letters, Volume 74
      Author(s): Didier Clamond
      This short note is about the gauge condition for the velocity potential, the definitions of the Bernoulli constant and of the velocity speeds in the context of water waves. These definitions are often implicit and thus the source of confusion in the literature. This note aims at addressing this issue. The discussion is related to water waves because the confusion are frequent in this field, but it is relevant for more general problems in fluid mechanics.

      PubDate: 2017-06-21T15:35:37Z
      DOI: 10.1016/j.aml.2017.05.018
      Issue No: Vol. 74 (2017)
       
  • Asymptotical boundedness and stability for stochastic differential
           equations with delay driven by G-Brownian motion
    • Authors: Wensheng Yin; Yong Ren
      Pages: 121 - 126
      Abstract: Publication date: December 2017
      Source:Applied Mathematics Letters, Volume 74
      Author(s): Wensheng Yin, Yong Ren
      The purpose of this paper is to discuss a class of stochastic differential equations with delay driven by G -Brownian motion ( G -SDDEs, in short). The asymptotical boundedness and exponential stability of the equations are obtained by means of G -Lyapunov function. An example is proposed to illustrate the theory obtained.

      PubDate: 2017-07-02T15:46:14Z
      DOI: 10.1016/j.aml.2017.06.001
      Issue No: Vol. 74 (2017)
       
  • Attractors for the Kirchhoff equations with strong nonlinear damping
    • Authors: Honglv Ma; Chengkui Zhong
      Pages: 127 - 133
      Abstract: Publication date: December 2017
      Source:Applied Mathematics Letters, Volume 74
      Author(s): Honglv Ma, Chengkui Zhong
      In this paper we obtain the existence of a global attractor for the Kirchhoff equations with strong nonlinear damping, which attracts every H 0 1 ( Ω ) × L 2 ( Ω ) -bounded set with respect to the H 0 1 ( Ω ) × H 0 1 ( Ω ) norm.

      PubDate: 2017-07-02T15:46:14Z
      DOI: 10.1016/j.aml.2017.06.002
      Issue No: Vol. 74 (2017)
       
  • Global well-posedness of solutions for magnetohydrodynamics-α model
           in R3
    • Authors: Xiaopeng Zhao; Jinde Cao
      Pages: 134 - 139
      Abstract: Publication date: December 2017
      Source:Applied Mathematics Letters, Volume 74
      Author(s): Xiaopeng Zhao, Jinde Cao
      In this paper, by using Strauss’ inequality, we prove the existence of global mild solutions to the 3D magnetohydrodynamics- α equations with small initial data.

      PubDate: 2017-07-02T15:46:14Z
      DOI: 10.1016/j.aml.2017.05.021
      Issue No: Vol. 74 (2017)
       
  • Fractional Kirchhoff equation with a general critical nonlinearity
    • Authors: Hua Jin; Wenbin Liu
      Pages: 140 - 146
      Abstract: Publication date: December 2017
      Source:Applied Mathematics Letters, Volume 74
      Author(s): Hua Jin, Wenbin Liu
      In this paper, for any dimension N > 2 s ( 0 < s < 1 ) , we study the fractional Kirchhoff equation a + b ∫ R N ( − Δ ) s 2 u 2 d x ( − Δ ) s u + u = f ( u ) in R N , with a critical nonlinearity, where ( − Δ ) s is the fractional Laplacian. By using a perturbation approach, we prove the existence of solutions to the above problem without the Ambrosetti–Rabinowitz condition when the parameter b is small. Moreover, we obtain the asymptotic behavior of solutions as b → 0 . The method we use and the result we get are applicable in any dimension N > 2 s . Our result improves the study made in the low dimension 2 s < N < 4 s .

      PubDate: 2017-07-02T15:46:14Z
      DOI: 10.1016/j.aml.2017.06.003
      Issue No: Vol. 74 (2017)
       
  • Hyers–Ulam stability of the time independent Schrödinger
           equations
    • Authors: Soon-Mo Jung; Jaiok Roh
      Pages: 147 - 153
      Abstract: Publication date: December 2017
      Source:Applied Mathematics Letters, Volume 74
      Author(s): Soon-Mo Jung, Jaiok Roh
      In Jung and Roh (2017), we investigated some properties of approximate solutions of the second-order inhomogeneous linear differential equations. In this paper as an application of above paper we will study the stability of the time independent Schrödinger equation with a potential box of finite walls.

      PubDate: 2017-07-02T15:46:14Z
      DOI: 10.1016/j.aml.2017.05.020
      Issue No: Vol. 74 (2017)
       
  • Global existence, uniqueness and estimates of the solution to the
           Navier–Stokes equations
    • Authors: Alexander G. Ramm
      Pages: 154 - 160
      Abstract: Publication date: December 2017
      Source:Applied Mathematics Letters, Volume 74
      Author(s): Alexander G. Ramm
      The Navier–Stokes (NS) problem consists of finding a vector-function v from the Navier–Stokes equations. The solution v to NS problem is defined in this paper as the solution to an integral equation. The kernel G of this equation solves a linear problem which is obtained from the NS problem by dropping the nonlinear term ( v ⋅ ∇ ) v . The kernel G is found in closed form. Uniqueness of the solution to the integral equation is proved in a class of solutions v with finite norm N 1 ( v ) = sup ξ ∈ R 3 , t ∈ [ 0 , T ] ( 1 + ξ ) ( v + ∇ v ) ≤ c ( ∗ ) , where T > 0 and C > 0 are arbitrary large fixed constants. In the same class of solutions existence of the solution is proved under some assumption. Estimate of the energy of the solution is given.

      PubDate: 2017-07-02T15:46:14Z
      DOI: 10.1016/j.aml.2017.05.009
      Issue No: Vol. 74 (2017)
       
  • Factorization method applied to the second order difference equations
    • Authors: Alina Dobrogowska; Grzegorz Jakimowicz
      Pages: 161 - 166
      Abstract: Publication date: December 2017
      Source:Applied Mathematics Letters, Volume 74
      Author(s): Alina Dobrogowska, Grzegorz Jakimowicz
      The main purpose of this work is to apply the factorization method to difference equations. The factorization method offers the possibility of finding solutions of new classes of difference equations. We show how to integrate certain classes of second order difference equations. Finally, an example is presented to illustrate our main result.

      PubDate: 2017-07-02T15:46:14Z
      DOI: 10.1016/j.aml.2017.05.022
      Issue No: Vol. 74 (2017)
       
  • Small perturbations of elliptic problems with variable growth
    • Authors: Nejmeddine Chorfi; Vicenţiu D. Rădulescu
      Pages: 167 - 173
      Abstract: Publication date: December 2017
      Source:Applied Mathematics Letters, Volume 74
      Author(s): Nejmeddine Chorfi, Vicenţiu D. Rădulescu
      This paper deals with the study of a nonlinear eigenvalue problem driven by a new class of non-homogeneous differential operators with variable exponent and involving a nonlinear term with variable growth. The framework in the present paper corresponds to the case of small perturbations of the nonlinear term. Combining variational arguments with energy estimates, we establish the existence of eigenvalues in a neighborhood of the origin. Our abstract setting includes several models described by nonhomogeneous differential operators, including the case of the capillarity equation.

      PubDate: 2017-07-02T15:46:14Z
      DOI: 10.1016/j.aml.2017.05.007
      Issue No: Vol. 74 (2017)
       
  • Convergence of Chebyshev type regularization method under Morozov
           discrepancy principle
    • Authors: Jun-Gang Wang; Yan Li; Yu-Hong Ran
      Pages: 174 - 180
      Abstract: Publication date: December 2017
      Source:Applied Mathematics Letters, Volume 74
      Author(s): Jun-Gang Wang, Yan Li, Yu-Hong Ran
      In this paper we investigate the convergence of Chebyshev type regularization strategy combined with the Morozov discrepancy principle, which is an a posteriori parameter choice rule and independent of the a priori information of exact solution. Compared with the standard Tikhonov regularization method, the Chebyshev type regularization method has no saturation restriction so that its convergence order holds for any υ ≥ 1 2 , where p = 2 υ + 1 2 υ in the H o ̈ l d e r type estimate.

      PubDate: 2017-07-02T15:46:14Z
      DOI: 10.1016/j.aml.2017.06.004
      Issue No: Vol. 74 (2017)
       
  • Blow-up phenomena for a nonlinear pseudo-parabolic equation with nonlocal
           source
    • Authors: Qunfei Long; Jianqing Chen
      Pages: 181 - 186
      Abstract: Publication date: December 2017
      Source:Applied Mathematics Letters, Volume 74
      Author(s): Qunfei Long, Jianqing Chen
      We discuss a class of quasi-linear pseudo-parabolic equation with nonlocal source u t − Δ u t − ∇ ⋅ ∇ u 2 q ∇ u = u p ( x , t ) ∫ Ω k ( x , y ) u p + 1 ( y , t ) d y x , y ∈ Ω , t ∈ ( 0 , T 0 ] , where q ≤ p and 0 < q < n − 2 2 . By establishing the criterions for blow-up, we determine the upper bounds for blow-up time under not only q < p and non-positive initial energy but also q = p and negative initial energy. The results show that the upper bound for blow-up time under q < p is different from it under q = p . Moreover, we also determine the lower bound for blow-up time.

      PubDate: 2017-07-02T15:46:14Z
      DOI: 10.1016/j.aml.2017.06.006
      Issue No: Vol. 74 (2017)
       
  • Preprocessing schemes for fractional-derivative problems to improve their
           convergence rates
    • Authors: Martin Stynes; José Luis Gracia
      Pages: 187 - 192
      Abstract: Publication date: December 2017
      Source:Applied Mathematics Letters, Volume 74
      Author(s): Martin Stynes, José Luis Gracia
      A simple and inexpensive preprocessing of an initial–boundary value problem with a Caputo time derivative is shown theoretically and numerically to yield an enhanced convergence rate for the L1 scheme. The same preprocessing can also be used with other methods for time-dependent problems.

      PubDate: 2017-07-02T15:46:14Z
      DOI: 10.1016/j.aml.2017.05.016
      Issue No: Vol. 74 (2017)
       
  • On invariance of schemes in the method of fundamental solutions
    • Authors: Koya Sakakibara; Shigetoshi Yazaki
      Abstract: Publication date: November 2017
      Source:Applied Mathematics Letters, Volume 73
      Author(s): Koya Sakakibara, Shigetoshi Yazaki
      Method of fundamental solutions (MFS) is a meshfree numerical solver for linear homogeneous partial differential equations, and it has been applied to several problems. It is well known that some numerical solutions by MFS do not satisfy invariance properties, which is unnatural from viewpoint of physics. In this paper, we propose a unified way to obtain invariant schemes for MFS. The key idea is to introduce scaling factors.

      PubDate: 2017-05-18T09:36:21Z
      DOI: 10.1016/j.aml.2017.04.018
      Issue No: Vol. 73 (2017)
       
  • A note on the stationary distribution of the stochastic chemostat model
           with general response functions
    • Authors: Liang Wang; Daqing Jiang
      Abstract: Publication date: November 2017
      Source:Applied Mathematics Letters, Volume 73
      Author(s): Liang Wang, Daqing Jiang
      A model of the chemostat involving stochastic perturbation is considered. Instead of assuming the familiar Monod kinetics for nutrient uptake, a general class of functions is used which includes both monotone and non-monotone uptake functions. Using the stochastic Lyapunov analysis method, under restrictions on the intensity of the noise, we show the existence of a stationary distribution and the ergodicity of the stochastic system.

      PubDate: 2017-05-18T09:36:21Z
      DOI: 10.1016/j.aml.2017.04.029
      Issue No: Vol. 73 (2017)
       
  • Asymptotic behavior for a generalized micropolar thermoelastic body
    • Authors: Marcio V. Ferreira; Jaime E. Muñoz Rivera; Amelie Rambaud; Octavio Vera
      Abstract: Publication date: November 2017
      Source:Applied Mathematics Letters, Volume 73
      Author(s): Marcio V. Ferreira, Jaime E. Muñoz Rivera, Amélie Rambaud, Octavio Vera
      The paper establishes the exponential stability of a micropolar thermoelastic homogeneous and linear body with frictional dissipation and thermal conduction of hyperbolic type, allowing for second sound. Existence and uniqueness are proved within the semigroup framework and stability is achieved thanks to a suitable Lyapunov functional.

      PubDate: 2017-05-18T09:36:21Z
      DOI: 10.1016/j.aml.2017.04.025
      Issue No: Vol. 73 (2017)
       
  • Stationary distribution and extinction of a stochastic SIR model with
           nonlinear perturbation
    • Authors: Qun Liu; Daqing Jiang
      Pages: 8 - 15
      Abstract: Publication date: November 2017
      Source:Applied Mathematics Letters, Volume 73
      Author(s): Qun Liu, Daqing Jiang
      In this paper, we analyze a stochastic SIR model with nonlinear perturbation. By the Lyapunov function method, we establish sufficient conditions for the existence of a unique ergodic stationary distribution of the model. Moreover, sufficient conditions for extinction of the disease are also obtained.

      PubDate: 2017-05-08T11:09:26Z
      DOI: 10.1016/j.aml.2017.04.021
      Issue No: Vol. 73 (2017)
       
  • Reconstructing a second-order Sturm–Liouville operator by an energetic
           boundary function iterative method
    • Authors: Chein-Shan Liu; Botong Li
      Pages: 49 - 55
      Abstract: Publication date: November 2017
      Source:Applied Mathematics Letters, Volume 73
      Author(s): Chein-Shan Liu, Botong Li
      We consider an inverse problem for reconstructing the second-order Sturm–Liouville operator with the help of boundary data. The concept of energetic boundary functions, which satisfy the given boundary conditions and preserve the energy, is introduced for the first time. Then, we can derive a linear system to recover the unknown important coefficients of leading coefficient and potential function through a few iterations. Two examples are given to verify the iterative method.

      PubDate: 2017-05-18T09:36:21Z
      DOI: 10.1016/j.aml.2017.04.023
      Issue No: Vol. 73 (2017)
       
  • Cahn–Hilliard on surfaces: A numerical study
    • Authors: P. Gera; D. Salac
      Pages: 56 - 61
      Abstract: Publication date: November 2017
      Source:Applied Mathematics Letters, Volume 73
      Author(s): P. Gera, D. Salac
      The Cahn–Hilliard system has been used to describe a wide number of phase separation processes, from co-polymer systems to lipid membranes. In this work the convergence properties of a closest-point based scheme are investigated. In place of solving the original fourth-order system directly, two coupled second-order systems are solved. The system is solved using an approximate Schur-decomposition as a preconditioner. The results indicate that with a sufficiently high-order time discretization the method only depends on the underlying spatial resolution.

      PubDate: 2017-05-18T09:36:21Z
      DOI: 10.1016/j.aml.2017.02.021
      Issue No: Vol. 73 (2017)
       
  • Recovering the initial distribution for strongly damped wave equation
    • Authors: Nguyen Huy Tuan; Doan Vuong Nguyen; Vo Van Au; Daniel Lesnic
      Pages: 69 - 77
      Abstract: Publication date: November 2017
      Source:Applied Mathematics Letters, Volume 73
      Author(s): Nguyen Huy Tuan, Doan Vuong Nguyen, Vo Van Au, Daniel Lesnic
      We study for the first time the inverse backward problem for the strongly damped wave equation. First, we show that the problem is severely ill-posed in the sense of Hadamard. Then, under the a priori assumption on the exact solution belonging to a Gevrey space, we propose the Fourier truncation method for stabilizing the ill-posed problem. A stability estimate of logarithmic type is established.

      PubDate: 2017-05-18T09:36:21Z
      DOI: 10.1016/j.aml.2017.04.014
      Issue No: Vol. 73 (2017)
       
  • Towards physically admissible reduced-order solutions for
           convection–diffusion problems
    • Authors: Swetlana Giere; Volker John
      Pages: 78 - 83
      Abstract: Publication date: November 2017
      Source:Applied Mathematics Letters, Volume 73
      Author(s): Swetlana Giere, Volker John
      This note proposes, analyzes, and studies numerically a regularization approach in the computation of the initial condition for reduced-order models (ROMs) of convection–diffusion equations. The aim of this approach consists in reducing significantly spurious oscillations in the ROM solutions.

      PubDate: 2017-05-18T09:36:21Z
      DOI: 10.1016/j.aml.2017.03.022
      Issue No: Vol. 73 (2017)
       
  • Double-step scale splitting iteration method for a class of complex
           symmetric linear systems
    • Authors: Zhong Zheng; Feng-Lin Huang; Yu-Cheng Peng
      Pages: 91 - 97
      Abstract: Publication date: November 2017
      Source:Applied Mathematics Letters, Volume 73
      Author(s): Zhong Zheng, Feng-Lin Huang, Yu-Cheng Peng
      In this paper, a double-step scale splitting (DSS) iteration method is proposed to solve a class of complex symmetric of linear equation. Unconditional convergence result is established under appropriate restrictions. Two reciprocal optimal iteration parameters and the corresponding optimal convergence factor are also determined. Numerical experiments on a few model problems are used to verify the effectiveness of the DSS iteration method.

      PubDate: 2017-05-23T05:15:43Z
      DOI: 10.1016/j.aml.2017.04.017
      Issue No: Vol. 73 (2017)
       
  • Multiple solutions for the fourth-order elliptic equation with vanishing
           potential
    • Authors: Wen Zhang; Jian Zhang; Zhiming Luo
      Pages: 98 - 105
      Abstract: Publication date: November 2017
      Source:Applied Mathematics Letters, Volume 73
      Author(s): Wen Zhang, Jian Zhang, Zhiming Luo
      This paper is concerned with the following fourth-order elliptic equation Δ 2 u − Δ u + V ( x ) u = K ( x ) f ( u ) + μ ξ ( x ) u p − 2 u , x ∈ R N , u ∈ H 2 ( R N ) , where Δ 2 ≔ Δ ( Δ ) is the biharmonic operator, N ≥ 5 , V , K are nonnegative continuous functions and f is a continuous function with a quasicritical growth. By working in weighted Sobolev spaces and using a variational method, we prove that the above equation has two nontrivial solutions.

      PubDate: 2017-05-23T05:15:43Z
      DOI: 10.1016/j.aml.2017.04.030
      Issue No: Vol. 73 (2017)
       
  • Numerical approximation of the basic reproduction number for a class of
           age-structured epidemic models
    • Authors: Toshikazu Kuniya
      Pages: 106 - 112
      Abstract: Publication date: November 2017
      Source:Applied Mathematics Letters, Volume 73
      Author(s): Toshikazu Kuniya
      We are concerned with the numerical approximation of the basic reproduction number R 0 , which is the well-known epidemiological threshold value defined by the spectral radius of the next generation operator. For a class of age-structured epidemic models in infinite-dimensional spaces, R 0 has the abstract form and cannot be explicitly calculated in general. We discretize the linearized equation for the infective population into a system of ordinary differential equations in a finite n -dimensional space and obtain a corresponding threshold value R 0 , n , which can be explicitly calculated as the positive dominant eigenvalue of the next generation matrix. Under the compactness of the next generation operator, we show that R 0 , n → R 0 as n → + ∞ in terms of the spectral approximation theory.

      PubDate: 2017-05-23T05:15:43Z
      DOI: 10.1016/j.aml.2017.04.031
      Issue No: Vol. 73 (2017)
       
  • Discontinuous Galerkin methods for the incompressible flow with nonlinear
           leak boundary conditions of friction type
    • Authors: Feifei Jing; Jian Li; Zhangxin Chen; Wenjing Yan
      Pages: 113 - 119
      Abstract: Publication date: November 2017
      Source:Applied Mathematics Letters, Volume 73
      Author(s): Feifei Jing, Jian Li, Zhangxin Chen, Wenjing Yan
      This work aims at employing the discontinuous Galerkin (DG) methods for the incompressible flow with nonlinear leak boundary conditions of friction type, whose continuous variational problem is an inequality due to the subdifferential property of such boundary conditions. Error estimates are derived for the velocity and pressure in the corresponding norms, this work ends with numerical results to demonstrate the theoretically predicted convergence orders and reflect the leak or non-leak phenomena.

      PubDate: 2017-05-23T05:15:43Z
      DOI: 10.1016/j.aml.2017.03.017
      Issue No: Vol. 73 (2017)
       
  • Fourth-order numerical method for the space–time tempered fractional
           diffusion-wave equation
    • Authors: Mehdi Dehghan; Mostafa Abbaszadeh; Weihua Deng
      Pages: 120 - 127
      Abstract: Publication date: November 2017
      Source:Applied Mathematics Letters, Volume 73
      Author(s): Mehdi Dehghan, Mostafa Abbaszadeh, Weihua Deng
      The main aim of the current paper is to develop a high-order numerical scheme to solve the space–time tempered fractional diffusion-wave equation. The convergence order of the proposed method is O ( τ 2 + h 4 ) . Also, we prove the unconditional stability and convergence of the developed method. The numerical results show the efficiency of the provided numerical scheme.

      PubDate: 2017-05-23T05:15:43Z
      DOI: 10.1016/j.aml.2017.04.011
      Issue No: Vol. 73 (2017)
       
  • Infinitely many sign-changing solutions for a class of biharmonic equation
           with p-Laplacian and Neumann boundary condition
    • Authors: Fenglong Sun; Lishan Liu; Yonghong Wu
      Pages: 128 - 135
      Abstract: Publication date: November 2017
      Source:Applied Mathematics Letters, Volume 73
      Author(s): Fenglong Sun, Lishan Liu, Yonghong Wu
      By introducing a subspace of H 2 ( Ω ) with constraints ∂ u ∂ n ∂ Ω = 0 and ∫ Ω u d x = 0 and using the Fountain Theorem, we obtain the existence of infinitely many sign-changing high energy solutions for a biharmonic equations with p -Laplacian and Neumann boundary condition.

      PubDate: 2017-05-28T06:23:28Z
      DOI: 10.1016/j.aml.2017.05.001
      Issue No: Vol. 73 (2017)
       
  • Residual symmetries and soliton-cnoidal wave interaction solutions for the
           negative-order Korteweg–de Vries equation
    • Authors: Junchao Chen; Shundong Zhu
      Pages: 136 - 142
      Abstract: Publication date: November 2017
      Source:Applied Mathematics Letters, Volume 73
      Author(s): Junchao Chen, Shundong Zhu
      The residual symmetry is derived for the negative-order Korteweg–de Vries equation from the truncated Painlevé expansion. This nonlocal symmetry is transformed into the Lie point symmetry and the finite symmetry transformation is presented. The multiple residual symmetries are constructed and localized by introducing new auxiliary variables, and then n th Bäcklund transformation in terms of determinant is provided. With the help of the consistent tanh expansion (CTE) method, the explicit soliton-cnoidal wave interaction solutions are obtained from the last consistent differential equation.

      PubDate: 2017-05-28T06:23:28Z
      DOI: 10.1016/j.aml.2017.05.002
      Issue No: Vol. 73 (2017)
       
  • Looking at a nonlinear inhomogeneous optical fiber through the generalized
           higher-order variable-coefficient Hirota equation
    • Authors: Xin-Yi Gao
      Pages: 143 - 149
      Abstract: Publication date: November 2017
      Source:Applied Mathematics Letters, Volume 73
      Author(s): Xin-Yi Gao
      Optical fiber communication system is one of the core supporting systems of the modern internet age, and studies on the ultrashort optical pulses are at the forefront of fiber optics, modern optics and optical engineering. Hereby, symbolic computation on the recently-proposed generalized higher-order variable-coefficient Hirota equation is performed, for certain ultrashort optical pulses propagating in a nonlinear inhomogeneous fiber. For the complex envelope function associated with the optical-pulse electric field in the fiber, an auto-Bäcklund transformation is worked out, along with a family of the analytic solutions. Both our Bäcklund transformation and analytic solutions depend on the optical-fiber variable coefficients which represent the effects of the first-order dispersion, second-order dispersion, third-order dispersion, Kerr nonlinearity, time delaying, phase modulation and gain/loss. Relevant constraints among those coefficients are also presented. We expect that the work could be of some use for the fiber-optics investigations.

      PubDate: 2017-05-28T06:23:28Z
      DOI: 10.1016/j.aml.2017.03.020
      Issue No: Vol. 73 (2017)
       
  • Similarity solutions of nonlinear third-order dispersive PDEs: The first
           critical exponent
    • Abstract: Publication date: December 2017
      Source:Applied Mathematics Letters, Volume 74
      Author(s): Hüseyin Koçak
      This study investigates the behaviour of blow-up and global similarity solutions for the nonlinear dispersion equation (NDE), u t = ( u n u ) x x x ± ( u p − 1 u ) x x in R × R + , n > 0 and p > n + 1 , and attempts to give some aspects analytically and numerically. One can easily see that the proposed NDE is more complicated and hence more difficult than the corresponding semilinear equation. We will particularly pay attention to the first critical exponent p = p 0 = n + 2 , which helps us to simplify the rescaled nonlinear equation and compare with semilinear ones studied in the literature.

      PubDate: 2017-06-16T15:31:56Z
       
  • Oscillation of a linear delay differential equation with slowly varying
           coefficient
    • Authors: Pituk
      Abstract: Publication date: November 2017
      Source:Applied Mathematics Letters, Volume 73
      Author(s): Mihály Pituk
      A new sufficient condition is given for the oscillation of all solutions of a linear scalar delay differential equation with slowly varying and uniformly positive coefficient at infinity. Based on the celebrated Myshkis type necessary condition, we show that this new sufficient condition is sharp within the considered class of delay differential equations.

      PubDate: 2017-05-18T09:36:21Z
       
  • Variational approach to differential equations with not instantaneous
           impulses
    • Authors: Liang Bai; Juan Nieto
      Abstract: Publication date: November 2017
      Source:Applied Mathematics Letters, Volume 73
      Author(s): Liang Bai, Juan J. Nieto
      In this note we introduce the concept of a weak solution for a linear equation with not instantaneous impulses. We use the classical Lax–Milgram Theorem to reveal the variational structure of the problem and get the existence and uniqueness of weak solutions as critical points. This will allow us in the future to deal with the corresponding nonlinear problems.

      PubDate: 2017-05-18T09:36:21Z
       
  • Oscillatory behavior of the second order noncanonical differential
           equations
    • Abstract: Publication date: November 2017
      Source:Applied Mathematics Letters, Volume 73
      Author(s): J. Džurina
      We establish new comparison theorem for deducing oscillation of noncanonical nonlinear differential equation r ( t ) u ′ ( t ) γ ′ + p ( t ) u γ ( τ ( t ) ) = 0 from that of suitable linear equation y ″ ( t ) + p ˜ ( t ) u ( τ ˜ ( t ) ) = 0 . Our results are based on Trench’s theory of canonical operators and comparison technique.

      PubDate: 2017-05-18T09:36:21Z
       
  • On asymptotic relationships between two higher order dynamic equations on
           time scales
    • Authors: Pavel
      Abstract: Publication date: November 2017
      Source:Applied Mathematics Letters, Volume 73
      Author(s): Pavel Řehák
      We consider the n th order dynamic equations x Δ n + p 1 ( t ) x Δ n − 1 + ⋯ + p n ( t ) x = 0 and y Δ n + p 1 ( t ) y Δ n − 1 + ⋯ + p n ( t ) y = f ( t , y ( τ ( t ) ) ) on a time scale T , where τ is a composition of the forward jump operators, p i are real rd-continuous functions and f is a continuous function; T is assumed to be unbounded above. We establish conditions that guarantee asymptotic equivalence between some solutions of these equations. No restriction is placed on whether the solutions are oscillatory or nonoscillatory. Applications to second order Emden–Fowler type dynamic equations and Euler type dynamic equations are shown.

      PubDate: 2017-05-18T09:36:21Z
       
 
 
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