Subjects -> MATHEMATICS (Total: 1013 journals)
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MATHEMATICS (714 journals)            First | 1 2 3 4     

Showing 401 - 538 of 538 Journals sorted alphabetically
Journal of Mathematical and Fundamental Sciences     Open Access  
Journal of Mathematical Behavior     Hybrid Journal   (Followers: 6)
Journal of Mathematical Chemistry     Hybrid Journal   (Followers: 5)
Journal of Mathematical Finance     Open Access   (Followers: 6)
Journal of Mathematical Imaging and Vision     Hybrid Journal   (Followers: 6)
Journal of Mathematical Logic     Hybrid Journal   (Followers: 2)
Journal of Mathematical Sciences     Hybrid Journal  
Journal of Mathematical Sciences and Applications     Open Access   (Followers: 2)
Journal of Mathematical Sociology     Hybrid Journal   (Followers: 3)
Journal of Mathematics     Open Access  
Journal of Mathematics and Statistics     Open Access   (Followers: 6)
Journal of Mathematics and Statistics Studies     Open Access  
Journal of Mathematics and the Arts     Hybrid Journal   (Followers: 1)
Journal of Mathematics Education at Teachers College     Open Access   (Followers: 5)
Journal of Mathematics in Industry     Open Access  
Journal of Mathematics Research     Open Access  
Journal of Metallurgy     Open Access   (Followers: 8)
Journal of Modern Mathematics Frontier     Open Access  
Journal of Multidisciplinary Modeling and Optimization     Open Access   (Followers: 1)
Journal of Multivariate Analysis     Hybrid Journal   (Followers: 15)
Journal of Nonlinear Analysis and Optimization : Theory & Applications     Open Access   (Followers: 4)
Journal of Nonlinear Mathematical Physics     Hybrid Journal   (Followers: 2)
Journal of Nonlinear Science     Hybrid Journal   (Followers: 1)
Journal of Numerical Cognition     Open Access   (Followers: 1)
Journal of Optimization     Open Access   (Followers: 5)
Journal of Peridynamics and Nonlocal Modeling     Hybrid Journal  
Journal of Progressive Research in Mathematics     Open Access   (Followers: 1)
Journal of Pseudo-Differential Operators and Applications     Hybrid Journal  
Journal of Pure and Applied Algebra     Full-text available via subscription   (Followers: 3)
Journal of Quantitative Linguistics     Hybrid Journal   (Followers: 6)
Journal of Scientific Computing     Hybrid Journal   (Followers: 19)
Journal of Scientific Research     Open Access  
Journal of Symbolic Computation     Hybrid Journal   (Followers: 2)
Journal of the Australian Mathematical Society     Full-text available via subscription  
Journal of the Egyptian Mathematical Society     Open Access  
Journal of the Indian Mathematical Society     Hybrid Journal  
Journal of the Institute of Mathematics of Jussieu     Hybrid Journal  
Journal of the London Mathematical Society     Hybrid Journal   (Followers: 3)
Journal of the Nigerian Mathematical Society     Open Access  
Journal of Theoretical and Applied Physics     Open Access   (Followers: 9)
Journal of Topology and Analysis     Hybrid Journal  
Journal of Transport and Supply Chain Management     Open Access   (Followers: 10)
Journal of Turbulence     Hybrid Journal   (Followers: 7)
Journal of Universal Mathematics     Open Access  
Journal of Urban Regeneration & Renewal     Full-text available via subscription   (Followers: 8)
JRAMathEdu : Journal of Research and Advances in Mathematics Education     Open Access   (Followers: 5)
JUMLAHKU : Jurnal Matematika Ilmiah STKIP Muhammadiyah Kuningan     Open Access  
JURING (Journal for Research in Mathematics Learning)     Open Access  
Jurnal Didactical Mathematics     Open Access   (Followers: 4)
Jurnal Matematika     Open Access  
Jurnal Matematika, Sains, Dan Teknologi     Open Access  
Jurnal Natural     Open Access  
Jurnal Pendidikan Matematika Raflesia     Open Access  
Jurnal Penelitian Pembelajaran Matematika Sekolah     Open Access  
Jurnal Penelitian Sains (JPS)     Open Access  
Jurnal Riset Pendidikan Matematika     Open Access  
Jurnal Sains Matematika dan Statistika     Open Access  
Jurnal Tadris Matematika     Open Access  
Jurnal Teknologi dan Sistem Komputer     Open Access  
Kontinu : Jurnal Penelitian Didaktik Matematika     Open Access  
Kreano, Jurnal Matematika Kreatif-Inovatif     Open Access  
Le Matematiche     Open Access  
Lettera Matematica     Hybrid Journal  
Lietuvos Matematikos Rinkinys     Open Access  
Limits : Journal of Mathematics and Its Applications     Open Access  
Linear Algebra and its Applications     Full-text available via subscription   (Followers: 22)
Linear and Multilinear Algebra     Hybrid Journal   (Followers: 7)
Lithuanian Mathematical Journal     Hybrid Journal  
Lobachevskii Journal of Mathematics     Open Access  
Logic Journal of the IGPL     Hybrid Journal   (Followers: 1)
Logica Universalis     Hybrid Journal  
manuscripta mathematica     Hybrid Journal   (Followers: 1)
MaPan : Jurnal Matematika dan Pembelajaran     Open Access  
Marine Genomics     Hybrid Journal   (Followers: 1)
Matemáticas, Educación y Sociedad     Open Access  
Matematicheskie Zametki     Full-text available via subscription  
Mathematica Scandinavica     Full-text available via subscription   (Followers: 1)
Mathematical Analysis and its Contemporary Applications     Open Access   (Followers: 1)
Mathematical Communications     Open Access  
Mathematical Computation     Open Access   (Followers: 1)
Mathematical Geosciences     Hybrid Journal   (Followers: 4)
Mathematical Journal of Interdisciplinary Sciences     Open Access   (Followers: 1)
Mathematical Medicine and Biology: A Journal of the IMA     Hybrid Journal   (Followers: 1)
Mathematical Methods in the Applied Sciences     Hybrid Journal   (Followers: 4)
Mathematical Methods of Statistics     Hybrid Journal   (Followers: 4)
Mathematical Modelling and Analysis     Open Access   (Followers: 1)
Mathematical Modelling of Natural Phenomena     Open Access   (Followers: 1)
Mathematical Models and Methods in Applied Sciences     Hybrid Journal   (Followers: 1)
Mathematical Notes     Hybrid Journal  
Mathematical Proceedings of the Cambridge Philosophical Society     Full-text available via subscription   (Followers: 2)
Mathematical Programming Computation     Hybrid Journal   (Followers: 2)
Mathematical Sciences     Open Access  
Mathematical Social Sciences     Hybrid Journal   (Followers: 1)
Mathematical Theory and Modeling     Open Access   (Followers: 6)
Mathematical Thinking and Learning     Hybrid Journal   (Followers: 4)
Mathematics and Statistics     Open Access   (Followers: 2)
Mathematics Education Forum Chitwan     Open Access   (Followers: 1)
Mathematics Education Journal     Open Access   (Followers: 4)
Mathematics Education Research Journal     Partially Free   (Followers: 16)
Mathematics of Control, Signals, and Systems (MCSS)     Hybrid Journal   (Followers: 5)
Mathematics Teacher: Learning and Teaching PK-12     Full-text available via subscription   (Followers: 9)
Mathematics Teaching in the Middle School     Full-text available via subscription   (Followers: 8)
Mathematische Annalen     Hybrid Journal   (Followers: 2)
Mathematische Nachrichten     Hybrid Journal   (Followers: 1)
Mathematische Semesterberichte     Hybrid Journal  
Mathematische Zeitschrift     Hybrid Journal   (Followers: 2)
MATICS     Open Access  
Matrix Science Mathematic     Open Access   (Followers: 1)
Measurement Science Review     Open Access   (Followers: 3)
Mediterranean Journal of Mathematics     Hybrid Journal  
Memetic Computing     Hybrid Journal  
Mendel : Soft Computing Journal     Open Access  
Metaheuristics     Hybrid Journal  
Metals and Materials International     Hybrid Journal   (Followers: 1)
Metascience     Hybrid Journal   (Followers: 1)
Metrology and Instruments / Метрологія та прилади     Open Access  
Milan Journal of Mathematics     Hybrid Journal  
MLQ- Mathematical Logic Quarterly     Hybrid Journal   (Followers: 1)
Modelling in Civil and Environmental Engineering     Open Access   (Followers: 4)
MONA : Matematik- og Naturfagsdidaktik     Hybrid Journal  
Monatshefte fur Mathematik     Hybrid Journal  
Moroccan Journal of Pure and Applied Analysis     Open Access  
Moscow University Mathematics Bulletin     Hybrid Journal  
MSOR Connections     Open Access   (Followers: 1)
Multiscale Modeling and Simulation     Hybrid Journal   (Followers: 2)
MUST : Journal of Mathematics Education, Science and Technology     Open Access   (Followers: 4)
Nagoya Mathematical Journal     Hybrid Journal   (Followers: 1)
Nano Research     Hybrid Journal   (Followers: 4)
Nanotechnologies in Russia     Hybrid Journal  
Natural Resource Modeling     Hybrid Journal  
New Mathematics and Natural Computation     Hybrid Journal   (Followers: 1)
Nonlinear Analysis     Hybrid Journal   (Followers: 1)
Nonlinear Analysis : Modelling and Control     Open Access   (Followers: 1)
Nonlinear Analysis: Hybrid Systems     Hybrid Journal  
Nonlinear Analysis: Real World Applications     Hybrid Journal   (Followers: 2)
Nonlinear Differential Equations and Applications NoDEA     Hybrid Journal  
North Carolina Journal of Mathematics and Statistics     Open Access  
Note di Matematica     Open Access  
NTM Zeitschrift für Geschichte der Wissenschaften, Technik und Medizin     Hybrid Journal   (Followers: 3)
Numeracy : Advancing Education in Quantitative Literacy     Open Access   (Followers: 1)
Numerical Analysis and Applications     Hybrid Journal   (Followers: 1)
Numerical Functional Analysis and Optimization     Hybrid Journal   (Followers: 3)
Numerical Linear Algebra with Applications     Hybrid Journal   (Followers: 7)
Numerische Mathematik     Hybrid Journal  
Open Journal of Discrete Mathematics     Open Access   (Followers: 3)
Open Journal of Modelling and Simulation     Open Access   (Followers: 2)
Operations Research Letters     Hybrid Journal   (Followers: 11)
Optimization Letters     Hybrid Journal   (Followers: 2)
Optimization Methods and Software     Hybrid Journal   (Followers: 6)
Opuscula Mathematica     Open Access  
Order     Hybrid Journal  
ORiON     Open Access  
P-Adic Numbers, Ultrametric Analysis, and Applications     Hybrid Journal  
PAMM : Proceedings in Applied Mathematics and Mechanics     Free  
Parallel Processing Letters     Hybrid Journal   (Followers: 3)
Peking Mathematical Journal     Hybrid Journal  
Periodica Mathematica Hungarica     Full-text available via subscription   (Followers: 1)
Petroleum Science     Open Access  
Philosophia Mathematica     Hybrid Journal   (Followers: 1)
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences     Full-text available via subscription   (Followers: 9)
PNA. Revista de Investigación en Didáctica de la Matemática     Open Access  
Polar Science     Hybrid Journal   (Followers: 3)
Positivity     Hybrid Journal  
Press Start     Open Access   (Followers: 1)
Prime Number     Full-text available via subscription  
Probability in the Engineering and Informational Sciences     Hybrid Journal   (Followers: 1)
Problemy Peredachi Informatsii     Full-text available via subscription  
Proceedings - Mathematical Sciences     Open Access   (Followers: 5)
Proceedings of the American Mathematical Society, Series B     Open Access   (Followers: 3)
Proceedings of the Edinburgh Mathematical Society     Hybrid Journal  
Proceedings of the Institution of Civil Engineers - Engineering and Computational Mechanics     Hybrid Journal   (Followers: 2)
Proceedings of the Latvian Academy of Sciences. Section B: Natural, Exact and Applied Sciences     Open Access   (Followers: 1)
Proceedings of the London Mathematical Society     Hybrid Journal   (Followers: 4)
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences     Full-text available via subscription   (Followers: 6)
Proceedings of the Royal Society of Edinburgh Section A Mathematics     Full-text available via subscription  
Proceedings of the Steklov Institute of Mathematics     Hybrid Journal  
Progress in Photovoltaics: Research & Applications     Hybrid Journal   (Followers: 6)
Proyecciones : Revista de Matematica     Open Access   (Followers: 1)
Publications Mathématiques de Besançon : Algèbre et Théorie des Nombres     Open Access  
Publications Mathématiques de L'IHÉS     Hybrid Journal   (Followers: 3)
Punjab University Journal of Mathematics     Open Access   (Followers: 2)
Pure Mathematics and Applications     Open Access  
Pythagoras     Open Access  
Quaestiones Mathematicae     Hybrid Journal  
Qualitative Theory of Dynamical Systems     Hybrid Journal  
Quantum Studies : Mathematics and Foundations     Hybrid Journal   (Followers: 2)
Quarterly Journal of Mathematics     Hybrid Journal  
Rare Metals     Hybrid Journal   (Followers: 2)
Recreational Mathematics Magazine     Open Access  
REDIMAT : Journal of Research in Mathematics Education     Open Access   (Followers: 6)
REMAT : Revista Eletrônica da Matemática     Open Access  
Rendiconti del Circolo Matematico di Palermo     Hybrid Journal  
Reportes Científicos de la FaCEN     Open Access  
Research in Mathematics Education     Hybrid Journal   (Followers: 13)
Research in Nondestructive Evaluation     Hybrid Journal   (Followers: 7)
Research in Number Theory     Hybrid Journal  
Research in the Mathematical Sciences     Open Access  
Research Journal of Pure Algebra     Open Access   (Followers: 1)
Researches in Mathematics     Open Access  
Results in Control and Optimization     Open Access  

  First | 1 2 3 4     

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Opuscula Mathematica
Journal Prestige (SJR): 0.378
Citation Impact (citeScore): 1
Number of Followers: 0  

  This is an Open Access Journal Open Access journal
ISSN (Print) 1232-9274 - ISSN (Online) 2300-6919
Published by AGH University of Science and Technology Press Homepage  [6 journals]
  • Existence of positive continuous weak solutions for some semilinear
           elliptic eigenvalue problems

    • Abstract:
      Author(s): Noureddine Zeddini, Rehab Saeed Sari.

      Abstract: Let \(D\) be a bounded \(C^{1,1}\)-domain in \(\mathbb{R}^d\), \(d\geq 2\). The aim of this article is twofold. The first goal is to give a new characterization of the Kato class of functions \(K(D)\) that was defined by N. Zeddini for \(d=2\) and by H. Mâagli and M. Zribi for \(d\geq 3\) and adapted to study some nonlinear elliptic problems in \(D\). The second goal is to prove the existence of positive continuous weak solutions, having the global behavior of the associated homogeneous problem, for sufficiently small values of the nonnegative constants \(\lambda\) and \(\mu\) to the following system \(\Delta u=\lambda f(x,u,v)\), \(\Delta v=\mu g(x,u,v)\) in \(D\), \(u=\phi_1\) and \(v=\phi_2\) on \(\partial D\), where \(\phi_1\) and \(\phi_2\) are nontrivial nonnegative continuous functions on \(\partial D\). The functions \(f\) and \(g\) are nonnegative and belong to a class of functions containing in particular all functions of the type \(f(x,u,v)=p(x) u^{\alpha}h_1(v)\) and \(g(x,u,v)=q(x)h_2(u)v^{\beta}\) with \(\alpha\geq 1\), \(\beta \geq 1\), \(h_1\), \(h_2\) are continuous on \([0,\infty)\) and \(p\), \(q\) are nonnegative functions in \(K(D)\).
      Keywords: Green function, Kato class, nonlinear elliptic systems, positive solution, maximum principle, Schauder fixed point theorem.
      Mathematics Subject Classification: 31A35, 31B35, 31A16, 35B09, 35B50, 35J08, 35J57.
      Journal: Opuscula Mathematica.
      Citation: Opuscula Math. 42, no. 3 (2022), 489-519, https://doi.org/10.7494/OpMath.2022.42.3.489.  
      PubDate: Fri, 29 Apr 2022 21:30:07 +020
       
  • Spectral resolutions for non-self-adjoint block convolution operators

    • Abstract:
      Author(s): Ewelina Zalot.

      Abstract: The paper concerns the spectral theory for a class of non-self-adjoint block convolution operators. We mainly discuss the spectral representations of such operators. It is considered the general case of operators defined on Banach spaces. The main results are applied to periodic Jacobi matrices.
      Keywords: spectral operators, chains, triangular decomposition, Laurent operators, Jacobi matrices.
      Mathematics Subject Classification: 47B40, 47B28, 47B36, 47B35, 47B39.
      Journal: Opuscula Mathematica.
      Citation: Opuscula Math. 42, no. 3 (2022), 459-487, https://doi.org/10.7494/OpMath.2022.42.3.459.  
      PubDate: Fri, 29 Apr 2022 21:30:06 +020
       
  • Distance irregularity strength of graphs with pendant vertices

    • Abstract:
      Author(s): Faisal Susanto, Kristiana Wijaya, Slamin, Andrea Semaničová-Feňovčíková.

      Abstract: A vertex \(k\)-labeling \(\phi:V(G)\rightarrow\{1,2,\dots,k\}\) on a simple graph \(G\) is said to be a distance irregular vertex \(k\)-labeling of \(G\) if the weights of all vertices of \(G\) are pairwise distinct, where the weight of a vertex is the sum of labels of all vertices adjacent to that vertex in \(G\). The least integer \(k\) for which \(G\) has a distance irregular vertex \(k\)-labeling is called the distance irregularity strength of \(G\) and denoted by \(\mathrm{dis}(G)\). In this paper, we introduce a new lower bound of distance irregularity strength of graphs and provide its sharpness for some graphs with pendant vertices. Moreover, some properties on distance irregularity strength for trees are also discussed in this paper.
      Keywords: vertex \(k\)-labeling, distance irregular vertex \(k\)-labeling, distance irregularity strength, pendant vertices.
      Mathematics Subject Classification: 05C78, 05C12.
      Journal: Opuscula Mathematica.
      Citation: Opuscula Math. 42, no. 3 (2022), 439-458, https://doi.org/10.7494/OpMath.2022.42.3.439.  
      PubDate: Fri, 29 Apr 2022 21:30:05 +020
       
  • On Ambarzumian type theorems for tree domains

    • Abstract:
      Author(s): Vyacheslav Pivovarchik.

      Abstract: It is known that the spectrum of the spectral Sturm-Liouville problem on an equilateral tree with (generalized) Neumann's conditions at all vertices uniquely determines the potentials on the edges in the unperturbed case, i.e. case of the zero potentials on the edges (Ambarzumian's theorem). This case is exceptional, and in general case (when the Dirichlet conditions are imposed at some of the pendant vertices) even two spectra of spectral problems do not determine uniquely the potentials on the edges. We consider the spectral Sturm-Liouville problem on an equilateral tree rooted at its pendant vertex with (generalized) Neumann conditions at all vertices except of the root and the Dirichlet condition at the root. In this case Ambarzumian's theorem can't be applied. We show that if the spectrum of this problem is unperturbed, the spectrum of the Neumann-Dirichlet problem on the root edge is also unperturbed and the spectra of the problems on the complimentary subtrees with (generalized) Neumann conditions at all vertices except the subtrees' roots and the Dirichlet condition at the subtrees' roots are unperturbed then the potential on each edge of the tree is 0 almost everywhere.
      Keywords: Sturm-Liouville equation, eigenvalue, equilateral tree, star graph, Dirichlet boundary condition, Neumann boundary condition.
      Mathematics Subject Classification: 34B45, 34B24, 34L20.
      Journal: Opuscula Mathematica.
      Citation: Opuscula Math. 42, no. 3 (2022), 427-437, https://doi.org/10.7494/OpMath.2022.42.3.427.  
      PubDate: Fri, 29 Apr 2022 21:30:04 +020
       
  • Growth of solutions of a class of linear fractional differential equations
           with polynomial coefficients

    • Abstract:
      Author(s): Saada Hamouda, Sofiane Mahmoudi.

      Abstract: This paper is devoted to the study of the growth of solutions of certain class of linear fractional differential equations with polynomial coefficients involving the Caputo fractional derivatives by using the generalized Wiman-Valiron theorem in the fractional calculus.
      Keywords: linear fractional differential equations, growth of solutions, Caputo fractional derivative operator.
      Mathematics Subject Classification: 34M10, 26A33.
      Journal: Opuscula Mathematica.
      Citation: Opuscula Math. 42, no. 3 (2022), 415-426, https://doi.org/10.7494/OpMath.2022.42.3.415.  
      PubDate: Fri, 29 Apr 2022 21:30:03 +020
       
  • New aspects for the oscillation of first-order difference equations with
           deviating arguments

    • Abstract:
      Author(s): Emad R. Attia, Bassant M. El-Matary.

      Abstract: We study the oscillation of first-order linear difference equations with non-monotone deviating arguments. Iterative oscillation criteria are obtained which essentially improve, extend, and simplify some known conditions. These results will be applied to some numerical examples.
      Keywords: difference equations, oscillation, non-monotone advanced arguments.
      Mathematics Subject Classification: 39A10, 39A21.
      Journal: Opuscula Mathematica.
      Citation: Opuscula Math. 42, no. 3 (2022), 393-413, https://doi.org/10.7494/OpMath.2022.42.3.393.  
      PubDate: Fri, 29 Apr 2022 21:30:02 +020
       
  • Monodromy invariant Hermitian forms for second order Fuchsian differential
           equations with four singularities

    • Abstract:
      Author(s): Shunya Adachi.

      Abstract: We study the monodromy invariant Hermitian forms for second order Fuchsian differential equations with four singularities. The moduli space of our monodromy representations can be realized by certain affine cubic surface. In this paper we characterize the irreducible monodromies having the non-degenerate invariant Hermitian forms in terms of that cubic surface. The explicit forms of invariant Hermitian forms are also given. Our result may bring a new insight into the study of the Painlevé differential equations.
      Keywords: Fuchsian differential equations, monodromy representation, monodromy invariant Hermitian form.
      Mathematics Subject Classification: 34M35, 34M15.
      Journal: Opuscula Mathematica.
      Citation: Opuscula Math. 42, no. 3 (2022), 361-391, https://doi.org/10.7494/OpMath.2022.42.3.361.  
      PubDate: Fri, 29 Apr 2022 21:30:01 +020
       
  • Ground states of coupled critical Choquard equations with weighted
           potentials

    • Abstract:
      Author(s): Gaili Zhu, Chunping Duan, Jianjun Zhang, Huixing Zhang.

      Abstract: In this paper, we are concerned with the following coupled Choquard type system with weighted potentials \[\begin{cases} -\Delta u+V_{1}(x)u=\mu_{1}(I_{\alpha}\!\ast\![Q(x) u ^{\frac{N+\alpha}{N}}])Q(x) u ^{\frac{\alpha}{N}-1}u+\beta(I_{\alpha}\!\ast\![Q(x) v ^{\frac{N+\alpha}{N}}])Q(x) u ^{\frac{\alpha}{N}-1}u,\\ -\Delta v+V_{2}(x)v=\mu_{2}(I_{\alpha}\!\ast\![Q(x) v ^{\frac{N+\alpha}{N}}])Q(x) v ^{\frac{\alpha}{N}-1}v+\beta(I_{\alpha}\!\ast\![Q(x) u ^{\frac{N+\alpha}{N}}])Q(x) v ^{\frac{\alpha}{N}-1}v,\\ u,v\in H^{1}(\mathbb{R}^{N}),\end{cases}\] where \(N\geq3\), \(\mu_{1},\mu_{2},\beta\gt 0\) and \(V_{1}(x)\), \(V_{2}(x)\) are nonnegative functions. Via the variational approach, one positive ground state solution of this system is obtained under some certain assumptions on \(V_{1}(x)\), \(V_{2}(x)\) and \(Q(x)\). Moreover, by using Hardy's inequality and one Pohozǎev identity, a non-existence result of non-trivial solutions is also considered.
      Keywords: ground states, Choquard equations, Hardy-Littlewood-Sobolev inequality, lower critical exponent.
      Mathematics Subject Classification: 35B25, 35B33, 35J61.
      Journal: Opuscula Mathematica.
      Citation: Opuscula Math. 42, no. 2 (2022), 337-354, https://doi.org/10.7494/OpMath.2022.42.2.337.  
      PubDate: Fri, 25 Feb 2022 14:30:09 +010
       
  • On some inverse problem for bi-parabolic equation with observed data in
           L^{p} spaces

    • Abstract:
      Author(s): Nguyen Huy Tuan.

      Abstract: The bi-parabolic equation has many practical significance in the field of heat transfer. The objective of the paper is to provide a regularized problem for bi-parabolic equation when the observed data are obtained in \(L^p\). We are interested in looking at three types of inverse problems. Regularization results in the \(L^2\) space appears in many related papers, but the survey results are rare in \(L^p\), \(p \neq 2\). The first problem related to the inverse source problem when the source function has split form. For this problem, we introduce the error between the Fourier regularized solution and the exact solution in \(L^p\) spaces. For the inverse initial problem for both linear and nonlinear cases, we applied the Fourier series truncation method. Under the terminal input data observed in \(L^p\), we obtain the approximated solution also in the space \(L^p\). Under some reasonable smoothness assumptions of the exact solution, the error between the the regularized solution and the exact solution are derived in the space \(L^p\). This paper seems to generalize to previous results for bi-parabolic equation on this direction.
      Keywords: bi-parabolic equations, Fourier truncation method, inverse source parabolic, inverse initial problem, Sobolev embeddings, Sobolev embeddings.
      Mathematics Subject Classification: 35A05, 35A08.
      Journal: Opuscula Mathematica.
      Citation: Opuscula Math. 42, no. 2 (2022), 305-335, https://doi.org/10.7494/OpMath.2022.42.2.305.  
      PubDate: Fri, 25 Feb 2022 14:30:08 +010
       
  • Entire solutions for some critical equations in the Heisenberg group

    • Abstract:
      Author(s): Patrizia Pucci, Letizia Temperini.

      : We complete the study started in the paper [P. Pucci, L.Temperini, On the concentration-compactness principle for Folland-Stein spaces and for fractional horizontal Sobolev spaces, Math. Eng. 5 (2023), Paper no. 007], giving some applications of its abstract results to get existence of solutions of certain critical equations in the entire Heinseberg group. In particular, different conditions for existence are given for critical horizontal \(p\)-Laplacian equations.
      Keywords: Heisenberg group, entire solutions, critical exponents.
      Mathematics Subject Classification: 35J62, 35J70, 35B08, 35J20, 35B09.
      Journal: Opuscula Mathematica.
      Citation: Opuscula Math. 42, no. 2 (2022), 279-303, https://doi.org/10.7494/OpMath.2022.42.2.279.  
      PubDate: Fri, 25 Feb 2022 14:30:07 +010
       
  • Double phase problems: a survey of some recent results

    • Abstract:
      Author(s): Nikolaos S. Papageorgiou.

      Abstract: We review some recent results on double phase problems. We focus on the relevant function space framework, which is provided by the generalized Orlicz spaces. We also describe the basic tools and methods used to deal with double phase problems, given that there is no global regularity theory for these problems.
      Keywords: double phase integrand, generalized Orlicz spaces, regularity theory, maximum principle, Nehari manifold.
      Mathematics Subject Classification: 35J20, 35J60.
      Journal: Opuscula Mathematica.
      Citation: Opuscula Math. 42, no. 2 (2022), 257-278, https://doi.org/10.7494/OpMath.2022.42.2.257.  
      PubDate: Fri, 25 Feb 2022 14:30:06 +010
       
  • Exponential decay of solutions to a class of fourth-order nonlinear
           hyperbolic equations modeling the oscillations of suspension bridges

    • Abstract:
      Author(s): Yang Liu, Chao Yang.

      Abstract: This paper is concerned with a class of fourth-order nonlinear hyperbolic equations subject to free boundary conditions that can be used to describe the nonlinear dynamics of suspension bridges.
      Keywords: fourth-order nonlinear hyperbolic equations, weak solutions, exponential decay, a family of potential wells.
      Mathematics Subject Classification: 35L35, 35D30, 35B40.
      Journal: Opuscula Mathematica.
      Citation: Opuscula Math. 42, no. 2 (2022), 239-255, https://doi.org/10.7494/OpMath.2022.42.2.239.  
      PubDate: Fri, 25 Feb 2022 14:30:05 +010
       
  • Blowup phenomena for some fourth-order strain wave equations at arbitrary
           positive initial energy level

    • Abstract:
      Author(s): Qiang Lin, Yongbing Luo.

      Abstract: In this paper, we study a series of fourth-order strain wave equations involving dissipative structure, which appears in elasto-plastic-microstructure models. By some differential inequalities, we derive the finite time blow up results and the estimates of the upper bound blowup time with arbitrary positive initial energy. We also discuss the influence mechanism of the linear weak damping and strong damping on blowup time, respectively.
      Keywords: fourth-order strain wave equation, arbitrary positive initial energy, blowup, blowup time.
      Mathematics Subject Classification: 35L05, 35A01, 35L55.
      Journal: Opuscula Mathematica.
      Citation: Opuscula Math. 42, no. 2 (2022), 219-238, https://doi.org/10.7494/OpMath.2022.42.2.219.  
      PubDate: Fri, 25 Feb 2022 14:30:04 +010
       
  • The d-bar formalism for the modified Veselov-Novikov equation on the
           half-plane

    • Abstract:
      Author(s): Guenbo Hwang, Byungsoo Moon.

      Abstract: We study the modified Veselov-Novikov equation (mVN) posed on the half-plane via the Fokas method, considered as an extension of the inverse scattering transform for boundary value problems. The mVN equation is one of the most natural \((2+1)\)-dimensional generalization of the \((1+1)\)-dimensional modified Korteweg-de Vries equation in the sense as to how the Novikov-Veselov equation is related to the Korteweg-de Vries equation. In this paper, by means of the Fokas method, we present the so-called global relation for the mVN equation, which is an algebraic equation coupled with the spectral functions, and the \(d\)-bar formalism, also known as Pompieu's formula. In addition, we characterize the \(d\)-bar derivatives and the relevant jumps across certain domains of the complex plane in terms of the spectral functions.
      Keywords: initial-boundary value problem, integrable nonlinear PDE, spectral analysis, \(d\)-bar.
      Mathematics Subject Classification: 35G31, 35Q53, 37K15.
      Journal: Opuscula Mathematica.
      Citation: Opuscula Math. 42, no. 2 (2022), 179-217, https://doi.org/10.7494/OpMath.2022.42.2.179.  
      PubDate: Fri, 25 Feb 2022 14:30:03 +010
       
  • Ground states for fractional nonlocal equations with logarithmic
           nonlinearity

    • Abstract:
      Author(s): Lifeng Guo, Yan Sun, Guannan Shi.

      Abstract: In this paper, we study on the fractional nonlocal equation with the logarithmic nonlinearity formed by \[\begin{cases}\mathcal{L}_{K}u(x)+u\log u + u ^{q-2}u=0, & x\in\Omega,\\ u=0, & x\in\mathbb{R}^{n}\setminus\Omega,\end{cases}\] where \(2\lt q\lt 2^{*}_s\), \(L_{K}\) is a non-local operator, \(\Omega\) is an open bounded set of \(\mathbb{R}^{n}\) with Lipschitz boundary. By using the fractional logarithmic Sobolev inequality and the linking theorem, we present the existence theorem of the ground state solutions for this nonlocal problem.
      Keywords: linking theorem, ground state, logarithmic nonlinearity, variational methods.
      Mathematics Subject Classification: 35J20, 35B33, 58E05.
      Journal: Opuscula Mathematica.
      Citation: Opuscula Math. 42, no. 2 (2022), 157-178, https://doi.org/10.7494/OpMath.2022.42.2.157.  
      PubDate: Fri, 25 Feb 2022 14:30:02 +010
       
  • Global existence and blow-up phenomenon for a quasilinear viscoelastic
           equation with strong damping and source terms

    • Abstract:
      Author(s): Huafei Di, Zefang Song.

      Abstract: Considered herein is the global existence and non-global existence of the initial-boundary value problem for a quasilinear viscoelastic equation with strong damping and source terms. Firstly, we introduce a family of potential wells and give the invariance of some sets, which are essential to derive the main results. Secondly, we establish the existence of global weak solutions under the low initial energy and critical initial energy by the combination of the Galerkin approximation and improved potential well method involving with \(t\). Thirdly, we obtain the finite time blow-up result for certain solutions with the non-positive initial energy and positive initial energy, and then give the upper bound for the blow-up time \(T^\ast\). Especially, the threshold result between global existence and non-global existence is given under some certain conditions. Finally, a lower bound for the life span \(T^\ast\) is derived by the means of integro-differential inequality techniques.
      Keywords: viscoelastic equation, strong damping and source, blow-up, upper and lower bounds, invariant set, potential well.
      Mathematics Subject Classification: 35L35, 35L75, 35R15.
      Journal: Opuscula Mathematica.
      Citation: Opuscula Math. 42, no. 2 (2022), 119-155, https://doi.org/10.7494/OpMath.2022.42.2.119.  
      PubDate: Fri, 25 Feb 2022 14:30:01 +010
       
  • All metric bases and fault-tolerant metric dimension for square of grid

    • Abstract:
      Author(s): Laxman Saha, Mithun Basak, Kalishankar Tiwary.

      Abstract: For a simple connected graph \(G=(V,E)\) and an ordered subset \(W = \{w_1,w_2,\ldots, w_k\}\) of \(V\), the code of a vertex \(v\in V\), denoted by \(\mathrm{code}(v)\), with respect to \(W\) is a \(k\)-tuple \((d(v,w_1),\ldots, d(v, w_k))\), where \(d(v, w_t)\) represents the distance between \(v\) and \(w_t\). The set \(W\) is called a resolving set of \(G\) if \(\mathrm{code}(u)\neq \mathrm{code}(v)\) for every pair of distinct vertices \(u\) and \(v\). A metric basis of \(G\) is a resolving set with the minimum cardinality. The metric dimension of \(G\) is the cardinality of a metric basis and is denoted by \(\beta(G)\). A set \(F\subset V\) is called fault-tolerant resolving set of \(G\) if \(F\setminus{\{v\}}\) is a resolving set of \(G\) for every \(v\in F\). The fault-tolerant metric dimension of \(G\) is the cardinality of a minimal fault-tolerant resolving set. In this article, a complete characterization of metric bases for \(G_{mn}^2\) has been given. In addition, we prove that the fault-tolerant metric dimension of \(G_{mn}^2\) is 4 if \(m+n\) is even. We also show that the fault-tolerant metric dimension of \(G_{mn}^2\) is at least 5 and at most 6 when \(m+n\) is odd.
      Keywords: code, resolving set, metric dimension, fault-tolerant resolving set, fault-tolerant metric dimension.
      Mathematics Subject Classification: 05C12, 05C05, 05C90, 05C76.
      Journal: Opuscula Mathematica.
      Citation: Opuscula Math. 42, no. 1 (2022), 93-111, https://doi.org/10.7494/OpMath.2022.42.1.93.  
      PubDate: Thu, 20 Jan 2022 18:00:06 +010
       
  • Solution of the boundary value problem of heat conduction in a cone

    • Abstract:
      Author(s): Murat Ramazanov, Muvasharkhan Jenaliyev, Nurtay Gulmanov.

      Abstract: In the paper we consider the boundary value problem of heat conduction in a non-cylindrical domain, which is an inverted cone, i.e. in the domain degenerating into a point at the initial moment of time. In this case, the boundary conditions contain a derivative with respect to the time variable; in practice, problems of this kind arise in the presence of the condition of the concentrated heat capacity. We prove a theorem on the solvability of a boundary value problem in weighted spaces of essentially bounded functions. The issues of solvability of the singular Volterra integral equation of the second kind, to which the original problem is reduced, are studied. We use the Carleman-Vekua method of equivalent regularization to solve the obtained singular Volterra integral equation.
      Keywords: noncylindrical domain, cone, boundary value problem of heat conduction, singular Volterra integral equation, Carleman-Vekua regularization method.
      Mathematics Subject Classification: 35K05, 45D99.
      Journal: Opuscula Mathematica.
      Citation: Opuscula Math. 42, no. 1 (2022), 75-91, https://doi.org/10.7494/OpMath.2022.42.1.75.  
      PubDate: Thu, 20 Jan 2022 18:00:05 +010
       
  • Edge homogeneous colorings

    • Abstract:
      Author(s): Tomáš Madaras, Alfréd Onderko, Thomas Schweser.

      Abstract: We explore four kinds of edge colorings defined by the requirement of equal number of colors appearing, in particular ways, around each vertex or each edge. We obtain the characterization of graphs colorable in such a way that the ends of each edge see (not regarding the edge color itself) \(q\) colors (resp. one end sees \(q\) colors and the color sets for both ends are the same), and a sufficient condition for 2-coloring a graph in a way that the ends of each edge see (with the omission of that edge color) altogether \(q\) colors. The relations of these colorings to \(M_q\)-colorings and role colorings are also discussed; we prove an interpolation theorem for the numbers of colors in edge coloring where all edges around each vertex have \(q\) colors.
      Keywords: homogeneous coloring, \(M_q\)-coloring, line graph, role coloring.
      Mathematics Subject Classification: 05C15.
      Journal: Opuscula Mathematica.
      Citation: Opuscula Math. 42, no. 1 (2022), 65-73, https://doi.org/10.7494/OpMath.2022.42.1.65.  
      PubDate: Thu, 20 Jan 2022 18:00:04 +010
       
  • Kneser-type oscillation criteria for second-order half-linear advanced
           difference equations

    • Abstract:
      Author(s): N. Indrajith, John R. Graef, E. Thandapani.

      Abstract: The authors present Kneser-type oscillation criteria for a class of advanced type second-order difference equations. The results obtained are new and they improve and complement known results in the literature. Two examples are provided to illustrate the importance of the main results.
      Keywords: second-order difference equations, advanced argument, half-linear, oscillation.
      Mathematics Subject Classification: 39A10.
      Journal: Opuscula Mathematica.
      Citation: Opuscula Math. 42, no. 1 (2022), 55-64, https://doi.org/10.7494/OpMath.2022.42.1.55.  
      PubDate: Thu, 20 Jan 2022 18:00:03 +010
       
  • γ-paired dominating graphs of cycles

    • Abstract:
      Author(s): Pannawat Eakawinrujee, Nantapath Trakultraipruk.

      Abstract: A paired dominating set of a graph \(G\) is a dominating set whose induced subgraph contains a perfect matching. The paired domination number, denoted by \(\gamma_{pr}(G)\), is the minimum cardinality of a paired dominating set of \(G\). A \(\gamma_{pr}(G)\)-set is a paired dominating set of cardinality \(\gamma_{pr}(G)\). The \(\gamma\)-paired dominating graph of \(G\), denoted by \(PD_{\gamma}(G)\), as the graph whose vertices are \(\gamma_{pr}(G)\)-sets. Two \(\gamma_{pr}(G)\)-sets \(D_1\) and \(D_2\) are adjacent in \(PD_{\gamma}(G)\) if there exists a vertex \(u\in D_1\) and a vertex \(v\notin D_1\) such that \(D_2=(D_1\setminus \{u\})\cup \{v\}\). In this paper, we present the \(\gamma\)-paired dominating graphs of cycles.
      Keywords: paired dominating graph, paired dominating set, paired domination number.
      Mathematics Subject Classification: 05C69, 05C38.
      Journal: Opuscula Mathematica.
      Citation: Opuscula Math. 42, no. 1 (2022), 31-54, https://doi.org/10.7494/OpMath.2022.42.1.31.  
      PubDate: Thu, 20 Jan 2022 18:00:02 +010
       
  • Uniqueness of solution of a nonlinear evolution dam problem in a
           heterogeneous porous medium

    • Abstract:
      Author(s): Messaouda Ben Attia, Elmehdi Zaouche, Mahmoud Bousselsal.

      Abstract: By choosing convenient test functions and using the method of doubling variables, we prove the uniqueness of the solution to a nonlinear evolution dam problem in an arbitrary heterogeneous porous medium of \(\mathbb{R}^n\) (\(n\in \{2,3\}\)) with an impermeable horizontal bottom.
      Keywords: test function, method of doubling variables, nonlinear evolution dam problem, heterogeneous porous medium, uniqueness.
      Mathematics Subject Classification: 35A02, 76S05.
      Journal: Opuscula Mathematica.
      Citation: Opuscula Math. 42, no. 1 (2022), 5-29, https://doi.org/10.7494/OpMath.2022.42.1.5.  
      PubDate: Thu, 20 Jan 2022 18:00:01 +010
       
 
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