Authors:Jaume Giné; Jaume Llibre Pages: 130 - 131 Abstract: Publication date: August 2017 Source:Applied Mathematics Letters, Volume 70 Author(s): Jaume Giné, Jaume Llibre We study the local analytic integrability for real Liénard systems, x ̇ = y − F ( x ) , y ̇ = x , with F ( 0 ) = 0 but F ′ ( 0 ) ≠ 0 , which implies that it has a strong saddle at the origin. First we prove that this problem is equivalent to study the local analytic integrability of the [ p : − q ] resonant saddles. This result implies that the local analytic integrability of a strong saddle is a hard problem and only partial results can be obtained. Nevertheless this equivalence gives a new method to compute the so-called resonant saddle quantities transforming the [ p : − q ] resonant saddle into a strong saddle.

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.

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.

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.

Authors:Guangyu Xu; Jun Zhou Pages: 1 - 7 Abstract: Publication date: November 2017 Source:Applied Mathematics Letters, Volume 73 Author(s): Guangyu Xu, Jun Zhou This paper gives the upper bounds of blow-up time and blow-up rate for a semi-linear edge-degenerate parabolic equation, and the results extend the results of a recent paper Chen and Liu (2016).

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

Authors:Stefan M. Filipov; Ivan D. Gospodinov; István Faragó Pages: 10 - 15 Abstract: Publication date: October 2017 Source:Applied Mathematics Letters, Volume 72 Author(s): Stefan M. Filipov, Ivan D. Gospodinov, István Faragó This paper presents a novel shooting method for solving two-point boundary value problems for second order ordinary differential equations. The method works as follows: first, a guess for the initial condition is made and an integration of the differential equation is performed to obtain an initial value problem solution; then, the end value of the solution is used in a simple iteration formula to correct the initial condition; the process is repeated until the second boundary condition is satisfied. The iteration formula is derived utilizing an auxiliary function that satisfies both boundary conditions and minimizes the H 1 semi-norm of the difference between itself and the initial value problem solution.

Authors:Zhong-Zhi Bai; Cun-Qiang Miao Pages: 23 - 28 Abstract: Publication date: October 2017 Source:Applied Mathematics Letters, Volume 72 Author(s): Zhong-Zhi Bai, Cun-Qiang Miao For the Hermitian eigenproblems, under proper assumption on an initial approximation to the desired eigenvector, we prove local quadratic convergence of the inexact simplified Jacobi–Davidson method when the involved relaxed correction equation is solved by a standard Krylov subspace iteration, which particularly leads to local cubic convergence when the relaxed correction equation is solved to a prescribed precision proportional to the norm of the current residual. These results are valid for the interior as well as the extreme eigenpairs of the Hermitian eigenproblem and, hence, generalize the results by Bai and Miao (2017) from the extreme eigenpairs to the interior ones.

Authors:Hongwu Wu; Baoguo Jia; Lynn Erbe Pages: 29 - 34 Abstract: Publication date: October 2017 Source:Applied Mathematics Letters, Volume 72 Author(s): Hongwu Wu, Baoguo Jia, Lynn Erbe This paper is concerned with oscillation of second order superlinear dynamic equations with oscillating coefficients. By using generalized Riccati transformations, oscillation theorems are obtained on an arbitrary time scale. We illustrate the versatility of our results by means of examples.

Authors:T.C. Hao; F.Z. Cong Pages: 42 - 49 Abstract: Publication date: October 2017 Source:Applied Mathematics Letters, Volume 72 Author(s): T.C. Hao, F.Z. Cong In this paper, we propose an efficient method for solving a class of BVPs with nonlocal boundary conditions. The main idea of our method is to obtain the approximate solutions by series representation via suitable base functions. We prove the convergence of the proposed method and give the error estimate. The proposed method is applied to solve two BVPs. The numerical results show that our algorithm is better as compared to the existing ones. Furthermore, our method can deal with linear and nonlinear problems both efficiently.

Authors:Xingqiu Zhang; Zhuyan Shao; Qiuyan Zhong Pages: 50 - 57 Abstract: Publication date: October 2017 Source:Applied Mathematics Letters, Volume 72 Author(s): Xingqiu Zhang, Zhuyan Shao, Qiuyan Zhong In this article, integrations of height functions of the nonlinear term on some special bounded sets are employed to investigate the existence and multiplicity of positive solutions for semipositone ( k , n − k ) conjugate boundary value problems. The interesting point lies in that singularities of the nonlinearity are related to both the time and the space variables.

Authors:Yong Zhou; Bashir Ahmad; Ahmed Alsaedi Pages: 70 - 74 Abstract: Publication date: October 2017 Source:Applied Mathematics Letters, Volume 72 Author(s): Yong Zhou, Bashir Ahmad, Ahmed Alsaedi In this paper, we present sufficient conditions for the existence of nonoscillatory solutions of the following fractional neutral functional differential equation D t α [ x ( t ) − c x ( t − τ ) ] + ∑ i = 1 m P i ( t ) x ( t − σ i ) = 0 , t ≥ t 0 , where D t α is Liouville fractional derivatives of order α ∈ [ 1 , + ∞ ) on the half-axis, c , τ , σ i ∈ ( 0 , + ∞ ) , P i ∈ C ( [ t 0 , + ∞ ) , R ) , m ≥ 1 is an integer.

Authors:Boris N. Chetverushkin; Nicola D’Ascenzo; Andrei V. Saveliev; Valeri I. Saveliev Pages: 75 - 81 Abstract: Publication date: October 2017 Source:Applied Mathematics Letters, Volume 72 Author(s): Boris N. Chetverushkin, Nicola D’Ascenzo, Andrei V. Saveliev, Valeri I. Saveliev We propose a new kinetically consistent method for the modelling of magneto gas dynamic processes. The algorithm is consistent with viscous, thermally conducting, resistive flows. Through a computational test we show that it is robust in resolving the physical behaviour of shock structures and instabilities.

Authors:Zhang Daoxiang; Ping Yan Pages: 1 - 5 Abstract: Publication date: September 2017 Source:Applied Mathematics Letters, Volume 71 Author(s): Zhang Daoxiang, Ping Yan In this paper we consider a predator–prey model with Leslie–Gower functional response. We present the necessary and sufficient conditions for the nonexistence of limit cycles by the application of the generalized Dulac theorem. As a result, we give the necessary and sufficient conditions for which the local asymptotic stability of the positive equilibrium implies the global stability for this model. Our results extend and improve the results presented by Aghajani and Moradifam (2006) and Hsu and Huang (1995).

Authors:Gabriela Holubová; Jakub Janoušek Pages: 6 - 13 Abstract: Publication date: September 2017 Source:Applied Mathematics Letters, Volume 71 Author(s): Gabriela Holubová, Jakub Janoušek This paper brings a revision of the so far known uniqueness result for a one-dimensional damped model of a suspension bridge. Using standard techniques, however with finer arguments, we provide a significant improvement and extension of the allowed interval for the stiffness parameter.

Authors:Mengwu Guo; Hongzhi Zhong Pages: 14 - 23 Abstract: Publication date: September 2017 Source:Applied Mathematics Letters, Volume 71 Author(s): Mengwu Guo, Hongzhi Zhong On the basis of the dual variational formulation of a class of elliptic variational inequalities, a constitutive relation error is defined for the variational inequalities as an a posteriori error estimator, which is shown to guarantee strict upper bounds of the global energy-norm errors of kinematically admissible solutions. A numerical example is presented to validate the strictly bounding property of the constitutive relation error for the variational inequalities in question.

Authors:Shugui Kang Pages: 24 - 29 Abstract: Publication date: September 2017 Source:Applied Mathematics Letters, Volume 71 Author(s): Shugui Kang We study the existence and the uniqueness of positive periodic solutions for a class of integral equationsof the form ϕ ( x ) = ∫ [ x , x + ω ] ∩ G K ( x , y ) [ f 1 ( y , ϕ ( y − τ ( y ) ) ) + f 2 ( y , ϕ ( y − τ ( y ) ) ) ] d y , x ∈ G , where G is a closed subset of R N with periodic structure. Our analysis relies on the fixed point theory for mixed monotone operator in Banach space.

Authors:John A.D. Appleby; Denis D. Patterson Pages: 30 - 37 Abstract: Publication date: September 2017 Source:Applied Mathematics Letters, Volume 71 Author(s): John A.D. Appleby, Denis D. Patterson In this letter, we obtain sharp estimates on the growth rate of solutions to a nonlinear ODE with a nonautonomous forcing term. The equation is superlinear in the state variable and hence solutions exhibit rapid growth and finite-time blow-up. The importance of ODEs of the type considered here stems from the key role they play in understanding the asymptotic behaviour of more complex systems involving delay and randomness.

Authors:Ferenc Izsák; Béla J. Szekeres Pages: 38 - 43 Abstract: Publication date: September 2017 Source:Applied Mathematics Letters, Volume 71 Author(s): Ferenc Izsák, Béla J. Szekeres Space-fractional diffusion problems are investigated from the modeling point of view. It is pointed out that the elementwise power of the Laplacian operator in R n is an inadequate model of fractional diffusion. Also, the approach with fractional calculus using zero extension is not a proper model of homogeneous Dirichlet boundary conditions. At the time, the spectral definition of the fractional Dirichlet Laplacian seems to be in many aspects a proper model of fractional diffusion.

Authors:Sunho Choi; Jaywan Chung; Yong-Jung Kim Pages: 51 - 58 Abstract: Publication date: September 2017 Source:Applied Mathematics Letters, Volume 71 Author(s): Sunho Choi, Jaywan Chung, Yong-Jung Kim Inviscid traveling waves are ghost-like phenomena that do not appear in reality because of their instability. However, they are the reason for the complexity of the traveling wave theory of reaction–diffusion equations and understanding them will help to resolve related puzzles. In this article, we obtain the existence, the uniqueness and the regularity of inviscid traveling waves under a general monostable nonlinearity that includes non-Lipschitz continuous reaction terms. Solution structures are obtained such as the thickness of the tail and the free boundaries.

Authors:Xin Jiang; Gang Meng; Zhikun She Pages: 59 - 66 Abstract: Publication date: September 2017 Source:Applied Mathematics Letters, Volume 71 Author(s): Xin Jiang, Gang Meng, Zhikun She In this paper, we investigate the existence of positive T -periodic solutions in a food web with one predator feeding on n preys by Leray–Schauder degree theory, which plays a significant role on further studying the uniqueness of limit cycles of this food web model. We start with a series of required spaces and operators and construct a bounded open set Ω over which the corresponding Leray–Schauder degree can be well-defined. Afterwards, by the invariance property of homotopy, we verify that the Leray–Schauder degree is not equal to 0 under certain conditions, thus implying the existence of positive T -periodic solutions. Finally, a numerical example is presented to illustrate our result.

Authors:Tieshan He; Yehui Huang; Kaihao Liang; Youfa Lei Pages: 67 - 73 Abstract: Publication date: September 2017 Source:Applied Mathematics Letters, Volume 71 Author(s): Tieshan He, Yehui Huang, Kaihao Liang, Youfa Lei We consider a nonlinear Neumann problem driven by a nonhomogeneous differential operator and an indefinite potential. Using variational methods together with flow invariance arguments, we show that the problem has at least one nodal solution. The result presented in this paper gives an answer to the open question raised by Papageorgiou and Rădulescu (2016).

Authors:Toka Diagana Pages: 74 - 80 Abstract: Publication date: September 2017 Source:Applied Mathematics Letters, Volume 71 Author(s): Toka Diagana In this paper we study the well-posedness for some damped elastic systems in a Banach space. To illustrate our abstract results, we study the existence of classical solutions to some elastic systems with viscous and strong dampings.

Authors:Abdul-Majid Wazwaz Pages: 1 - 6 Abstract: Publication date: August 2017 Source:Applied Mathematics Letters, Volume 70 Author(s): Abdul-Majid Wazwaz In this work we establish a two-mode modified Korteweg–de Vries equation (TmKdV). We show that multiple soliton solutions exist for specific values of the nonlinearity and dispersion parameters of this equation. We also derive more exact solutions for other values of these parameters. We will use the simplified Hirota’s method, the tanh/coth method to conduct this analysis.

Authors:Andrea N. Ceretani; Natalia N. Salva; Domingo A. Tarzia Pages: 14 - 17 Abstract: Publication date: August 2017 Source:Applied Mathematics Letters, Volume 70 Author(s): Andrea N. Ceretani, Natalia N. Salva, Domingo A. Tarzia This article is devoted to the proof of the existence and uniqueness of the modified error function introduced in Cho and Sunderland (1974). This function is defined as the solution to a nonlinear second order differential problem depending on a real parameter. We prove here that this problem has a unique non-negative analytic solution when the parameter assumes small positive values.

Authors:M.C. Leseduarte; R. Quintanilla; R. Racke Pages: 18 - 25 Abstract: Publication date: August 2017 Source:Applied Mathematics Letters, Volume 70 Author(s): M.C. Leseduarte, R. Quintanilla, R. Racke We study solutions for the one-dimensional problem of the Green–Lindsay and the Lord–Shulman theories with two temperatures. First, existence and uniqueness of weakly regular solutions are obtained. Second, we prove the exponential stability in the Green–Lindsay model, but the non-exponential stability for the Lord–Shulman model.

Authors:Zhongli Liu Pages: 26 - 31 Abstract: Publication date: August 2017 Source:Applied Mathematics Letters, Volume 70 Author(s): Zhongli Liu In this paper, we provide a criterion on the axial equilibrium to be globally asymptotically stable for the n -dimensional Gompertz system, i.e., only one species will survive and stabilize at its own carrying capacity, whilst all the other species are driven to extinction.

Authors:Juan Huang; Jian Zhang Pages: 32 - 38 Abstract: Publication date: August 2017 Source:Applied Mathematics Letters, Volume 70 Author(s): Juan Huang, Jian Zhang This paper concerns the exact value of cross-constrain problem and strong instability of standing waves in trapped dipolar quantum gases. By analyzing the characters of ground state, we give the relation of the cross-constrain problem and constrain problems. Then the exact value of the cross-constrain problem is obtained in the form of the ground state which is relevant to the frequency. Finally, we show the standing waves are strongly unstable.

Authors:Xiu-Bin Wang; Shou-Fu Tian; Chun-Yan Qin; Tian-Tian Zhang Pages: 40 - 47 Abstract: Publication date: October 2017 Source:Applied Mathematics Letters, Volume 72 Author(s): Xiu-Bin Wang, Shou-Fu Tian, Chun-Yan Qin, Tian-Tian Zhang Under investigation in this work is a generalized ( 3 + 1 )-dimensional Kadomtsev–Petviashvili equation, which can describe many nonlinear phenomena in fluid dynamics. By virtue of Bell’s polynomials, an effective and straightforward way is presented to explicitly construct its bilinear form and soliton solutions. Furthermore, based on the bilinear formalism, a direct method is employed to explicitly construct its rogue wave solutions with an ansätz function. Finally, the interaction phenomena between rogue waves and solitary waves are presented with a detailed derivation. The results can be used to enrich the dynamical behavior of higher dimensional nonlinear wave fields.

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.

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.

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.

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.

Abstract: Publication date: October 2017 Source:Applied Mathematics Letters, Volume 72 Author(s): B. Baculíková Establishing new properties of nonoscillatory solutions we introduce new oscillatory criteria for the second order advanced differential equation y ′ ′ ( t ) + p ( t ) y ( σ ( t ) ) = 0 . Our oscillatory results essentially extend the earlier ones. The progress is illustrated via Euler differential equation.

Authors:Ji-Huan Abstract: Publication date: October 2017 Source:Applied Mathematics Letters, Volume 72 Author(s): Ji-Huan He There exists NO classical variational principle for continuum dynamics so far. The well-known Hamilton’s principle is valid only for the conditions prescribed at the beginning and at the end of the motion and is therefore useless to deal with the usual initial-boundary condition problems. In this paper an exact classical variational theory is established, all initial conditions are converted into natural ones, furthermore, all natural final conditions automatically meet the physical requirements, leading to a vital innovation of Hamilton’s principle.

Authors:Kexue Abstract: Publication date: October 2017 Source:Applied Mathematics Letters, Volume 72 Author(s): Kexue Li We study the nonlinear fractional Schrödinger–Poissonequation ( − Δ ) s u + u + ϕ u = f ( x , u ) , in R 3 , ( − Δ ) t ϕ = u 2 , in R 3 , where s , t ∈ ( 0 , 1 ] , 2 t + 4 s > 3 . Under some assumptions on f , we obtain the existence of non-trivial solutions. The proof is based on the perturbation method and the mountain pass theorem.

Authors:Josef Abstract: Publication date: October 2017 Source:Applied Mathematics Letters, Volume 72 Author(s): Josef Diblík The paper is concerned with the long-term behavior of solutions to scalar nonlinear functional delayed differential equations y ̇ ( t ) = − f ( t , y t ) , t ≥ t 0 . It is assumed that f : [ t 0 , ∞ ) × C ↦ R is a continuous mapping satisfying a local Lipschitz condition with respect to the second argument and C ≔ C ( [ − r , 0 ] , R ) , r > 0 is the Banach space of continuous functions. The problem is solved of the existence of positive solutions if the equation is subjected to impulses y ( t s + ) = b s y ( t s ) , s = 1 , 2 , … , where t 0 ≤ t 1 < t 2 < ⋯ and b s > 0 , s = 1 , 2 , … . A criterion for the existence of positive solutions on [ t 0 − r , ∞ ) is proved and their upper estimates are given. Relations to previous results are discussed as well.

Authors:Lei Qiao Abstract: Publication date: September 2017 Source:Applied Mathematics Letters, Volume 71 Author(s): Lei Qiao Let a ( X , y ) be a nonnegative radical potential in a cylinder. In this paper, we study the solutions of the Dirichlet–Sch problem associated with a stationary Schrödinger operator. Existence of solutions for the Schrödinger equation and asymptotic properties as y → + ∞ and y → − ∞ are also considered under suitable conditions.

Authors:Fatma Abstract: Publication date: August 2017 Source:Applied Mathematics Letters, Volume 70 Author(s): Fatma Karakoç We investigate oscillation about the positive equilibrium point of a population model with piecewise constant argument. By using linearized oscillation theory for difference equations a necessary and sufficient condition for the oscillation is obtained. Moreover it is showed that every nonoscillatory solution approaches to the equilibrium point as t tends to infinity.