Authors:S.D. Akgöl; A. Zafer Pages: 1 - 7 Abstract: Publication date: February 2018 Source:Applied Mathematics Letters, Volume 76 Author(s): S.D. Akgöl, A. Zafer We initiate a study of the asymptotic integration problem for second-order nonlinear impulsive differential equations. It is shown that there exist solutions asymptotic to solutions of an associated linear homogeneous impulsive differential equation as in the case for equations without impulse effects. We introduce a new constructive method that can easily be applied to similar problems. An illustrative example is also given.

Authors:Maeddeh Pourbagher; Davod Khojasteh Salkuyeh Pages: 14 - 20 Abstract: Publication date: February 2018 Source:Applied Mathematics Letters, Volume 76 Author(s): Maeddeh Pourbagher, Davod Khojasteh Salkuyeh We present an iterative method for solving the complex symmetric system ( W + i T ) x = b , where T ∈ R n × n is a positive definite matrix and W ∈ R n × n is indefinite. Convergence of the method is investigated. The induced preconditioner is applied to accelerate the convergence rate of the GMRES( ℓ ) method and the numerical results are compared with those of the Hermitian normal splitting (HNS) preconditioner.

Authors:Mingliang Wang; Xiangzheng Li; Jinliang Zhang Pages: 21 - 27 Abstract: Publication date: February 2018 Source:Applied Mathematics Letters, Volume 76 Author(s): Mingliang Wang, Xiangzheng Li, Jinliang Zhang A nonlinear transformation to a generalized KP equation with general variable coefficients (gvcKP) has been derived by using the simplified homogeneous balance method (SHB). The nonlinear transformation converts gvcKP into a quadratic homogeneity equation to be solved. The quadratic homogeneity equation admits exponential function solutions, thus one-soliton and two-soliton solutions of gvcKP can be obtained by means of the nonlinear transformation derived in the paper. As the special cases of gvcKP, several generalized KP equations with different form and the corresponding results of them are also given.

Authors:Viatcheslav Priimenko; Mikhail Vishnevskii Pages: 28 - 33 Abstract: Publication date: February 2018 Source:Applied Mathematics Letters, Volume 76 Author(s): Viatcheslav Priimenko, Mikhail Vishnevskii There is studied a two-dimensional initial–boundary-value problem for the Lamé and Maxwell equations coupled through the nonlinear magnetoelastic effect. We prove the existence and uniqueness result.

Authors:Irina V. Alexandrova Pages: 34 - 39 Abstract: Publication date: February 2018 Source:Applied Mathematics Letters, Volume 76 Author(s): Irina V. Alexandrova The paper is devoted to the robust stability analysis of linear neutral type time delay systems with a constant delay and norm-bounded uncertainties. The method is based on the Lyapunov–Krasovskii functional with a derivative prescribed as a negative definite quadratic form of the “current” system state, which is considered to be not suitable for the robustness analysis due to the fact that it does not admit a quadratic lower bound. Unlike existing results, our approach does not require the derivative of the functional along the solutions of the perturbed system to be negative definite. Instead, we need just an essential part of the integral of the derivative to be negative. The resulting stability condition is presented in the form of a simple inequality depending on the so-called Lyapunov matrix, under an assumption that the difference operator of the perturbed system is stable. The result is applicable to all exponentially stable systems.

Authors:Pengyan Ding; Zhijian Yang; Yanan Li Pages: 40 - 45 Abstract: Publication date: February 2018 Source:Applied Mathematics Letters, Volume 76 Author(s): Pengyan Ding, Zhijian Yang, Yanan Li The paper investigates the existence of global attractor of Kirchhoff type equations with strong nonlinear damping: u t t − σ ( ‖ ∇ u ‖ 2 ) Δ u t − ϕ ( ‖ ∇ u ‖ 2 ) Δ u + f ( u ) = h ( x ) . It proves that when the growth exponent p of the nonlinearity f ( u ) is up to the supercritical range: N + 2 N − 2 ≡ p ∗ < p < p ∗ ∗ ≡ N + 4 ( N − 4 ) + ( N ≥ 3 ) , the related solution semigroup still has a global attractor (rather than a partially strong one as known before) in natural energy space.

Authors:Yan Zhang; Kuangang Fan; Shujing Gao; Shihua Chen Pages: 46 - 52 Abstract: Publication date: February 2018 Source:Applied Mathematics Letters, Volume 76 Author(s): Yan Zhang, Kuangang Fan, Shujing Gao, Shihua Chen In this paper, we propose and discuss a stochastic SIR epidemic model with saturated treatment and incidence rates. The existence and uniqueness of the global positive solution are achieved. By constructing suitable Lyapunov functions and using Khasminskii’s theory, we establish appropriate conditions to prove that the stochastic model has a unique stationary distribution and the ergodicity holds. Moreover, sufficient conditions that guarantee the epidemic disease’s extinction are given.

Authors:Yutong Chen; Jiabao Su Pages: 60 - 65 Abstract: Publication date: February 2018 Source:Applied Mathematics Letters, Volume 76 Author(s): Yutong Chen, Jiabao Su In this paper we obtain the existence of two one-sign nontrivial solutions for the fractional Laplacian equations with the nonlinearity having different asymptotic limits at infinity via the mountain pass theorem and the cut-off techniques.

Authors:Xiaoming Peng; Yadong Shang; Xiaoxiao Zheng Pages: 66 - 73 Abstract: Publication date: February 2018 Source:Applied Mathematics Letters, Volume 76 Author(s): Xiaoming Peng, Yadong Shang, Xiaoxiao Zheng This paper deals with a nonlinear viscoelastic wave equation with strong damping. Under certain conditions on the initial data and the relaxation function, a lower bound for the blow-up time is given by means of a first order differential inequality technique.

Authors:Shuhuang Xiang; Guidong Liu Pages: 74 - 80 Abstract: Publication date: February 2018 Source:Applied Mathematics Letters, Volume 76 Author(s): Shuhuang Xiang, Guidong Liu The optimal convergence rates on fast multipole methods (FMMs) for different Green’s functions are considered. Simpler convergence analysis and the more accurate convergence rates are presented.

Authors:Jamel Ben Amara; Jihed Hedhly Pages: 96 - 102 Abstract: Publication date: February 2018 Source:Applied Mathematics Letters, Volume 76 Author(s): Jamel Ben Amara, Jihed Hedhly We consider the Schrödinger equation − y ′ ′ + q ( x ) y = λ y , on a finite interval with Dirichlet boundary conditions, where q ( x ) is of indefinite sign. In the case of symmetric potentials, we prove the optimal lower bound λ n λ 1 ≥ n 2 (resp. upper bound λ n λ 1 ≤ n 2 ) for single-well q with λ 1 > 0 and μ 1 ≤ 0 (resp. single-barrier q and μ 1 ≥ 0 ), where μ 1 is the first eigenvalue of the Neumann boundary problem. In the case of nonsymmetric potentials, we prove the optimal lower bound λ 2 λ 1 ≥ 4 for single-well q with transition point at x = 1 2 , λ 1 > 0 and μ = max ( μ ˆ 1 , μ ̃ 1 ) ≤ 0 , where μ ˆ 1 and μ ̃ 1 are the first eigenvalues of the Neumann boundary problems defined on [ 0 , 1 2 ] and [ 1 2 , 1 ] , respectively.

Authors:Xiao Yang; Dianlou Du Pages: 110 - 116 Abstract: Publication date: February 2018 Source:Applied Mathematics Letters, Volume 76 Author(s): Xiao Yang, Dianlou Du A new spectral problem is introduced, which is indicated to be the negative counterpart of the mKdV spectral problem. Based on the fact, some integrable nonlinear evolution equations are obtained, including the derivative Schwarzian KdV equation, the mKdV5 equation and the sine–Gordon equation. Besides, Lax pairs and finite genus solutions of the equations are given.

Authors:Lin Zheng; Shu Wang Pages: 117 - 122 Abstract: Publication date: February 2018 Source:Applied Mathematics Letters, Volume 76 Author(s): Lin Zheng, Shu Wang In this paper we prove that for certain class of the initial data, the corresponding solutions of the 3-D viscous primitive equations without viscosity blow up in finite time. We find a specific solution to simplify the three dimensional systems, and furthermore, we construct a self-similar solution to solve the blow-up problem.

Authors:Andrei D. Polyanin; Inna K. Shingareva Pages: 123 - 129 Abstract: Publication date: February 2018 Source:Applied Mathematics Letters, Volume 76 Author(s): Andrei D. Polyanin, Inna K. Shingareva We consider blow-up problems having non-monotonic singular solutions that tend to infinity at a previously unknown point. For second-, third-, and fourth-order nonlinear ordinary differential equations, the corresponding multi-parameter test problems allowing exact solutions in elementary functions are proposed for the first time. A method of non-local transformations, that allows to numerically integrate non-monotonic blow-up problems, is described. A comparison of exact and numerical solutions showed the high efficiency of this method. It is important to note that the method of non-local transformations can be useful for numerical integration of other problems with large solution gradients (for example, in problems with solutions of boundary-layer type).

Authors:Nikolay A. Kudryashov; Roman B. Rybka; Aleksander G. Sboev Pages: 142 - 147 Abstract: Publication date: February 2018 Source:Applied Mathematics Letters, Volume 76 Author(s): Nikolay A. Kudryashov, Roman B. Rybka, Aleksander G. Sboev Analytical properties of the well-known FitzHugh–Nagumo model are studied. It is shown that the standard FitzHugh–Nagumo model does not pass the Painlevé test in the general case and does not have any meromorphic solutions because there are not any expansions of the general solution in the Laurent series. We demonstrate that the introduction of a nonlinear perturbation into the standard system of equations does not lead to the Painlevé property as well. However, in this case there are expansions of the general solution of the system of equations in the Laurent series for some values of parameters. This allows us to look for some exact solutions of the system of the perturbed FitzHugh–Nagumo model. We find some exact solutions of the perturbed FitzHugh–Nagumo system of equations in the form of kinks. These exact solutions can be used for testing numerical simulations of the system of equations corresponding to the FitzHugh–Nagumo model.

Authors:Jinmyoung Seok Pages: 148 - 156 Abstract: Publication date: February 2018 Source:Applied Mathematics Letters, Volume 76 Author(s): Jinmyoung Seok Consider nonlinear Choquard equations − Δ u + u = ( I α ∗ F ( u ) ) F ′ ( u ) in R N , lim x → ∞ u ( x ) = 0 , where I α denotes Riesz potential and α ∈ ( 0 , N ) . In this paper, we show that when F is doubly critical, i.e. F ( u ) = N N + α u N + α N + N − 2 N + α u N + α N − 2 , the nonlinear Choquard equation admits a nontrivial solution if N ≥ 5 and α + 4 < N .

Authors:Sergio Amat; Juan Ruiz; J. Carlos Trillo; Dionisio F. Yáñez Pages: 157 - 163 Abstract: Publication date: February 2018 Source:Applied Mathematics Letters, Volume 76 Author(s): Sergio Amat, Juan Ruiz, J. Carlos Trillo, Dionisio F. Yáñez In this paper sufficient conditions to determine if a stationary subdivision scheme produces Gibbs oscillations close to discontinuities are presented. It consists of the positivity of the partial sums of the values of the mask. We apply the conditions to non-negative masks and analyze (numerically when the sufficient conditions are not satisfied) the Gibbs phenomenon in classical and recent subdivision schemes like B-splines, Deslauriers and Dubuc interpolation subdivision schemes and the schemes proposed in Siddiqi and Ahmad (2008).

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.

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.

Authors:Sami Aouaoui Pages: 13 - 17 Abstract: Publication date: January 2018 Source:Applied Mathematics Letters, Volume 75 Author(s): Sami Aouaoui In this paper, we establish the existence of at least one nontrivial solution for a nonhomogeneous polyharmonic problem whose nonlinearity term is not necessarily continuous. Our main tool is a fixed point theorem for Banach semilattice.

Authors:Yueyue Li; Hengchun Hu Pages: 18 - 23 Abstract: Publication date: January 2018 Source:Applied Mathematics Letters, Volume 75 Author(s): Yueyue Li, Hengchun Hu The nonlocal symmetries for the Benjamin–Ono equation are obtained with the truncated Painlevé method. The nonlocal symmetries can be localized to the Lie point symmetries by introducing auxiliary dependent variables. The finite symmetry transformations related to the nonlocal symmetries are computed. The Benjamin–Ono equation is proved to be consistent Riccati solvable and many interaction solutions among solitons and other types of nonlinear excitations can be obtained by means of the consistent tanh expansion method with arbitrary constants.

Authors:Jianjun Chen; Wancheng Sheng Pages: 24 - 29 Abstract: Publication date: January 2018 Source:Applied Mathematics Letters, Volume 75 Author(s): Jianjun Chen, Wancheng Sheng In this paper, we are concerned with the simple waves for the two dimensional (2D) compressible Euler equations in magnetohydrodynamics. By using the sufficient conditions for the existence of characteristic decompositions to the general quasilinear strictly hyperbolic systems, we establish that any wave adjacent to a constant state must be a simple wave to the two dimensional compressible magnetohydrodynamics system for a polytropic Van der Waals gas and a polytropic perfect gas.

Authors:Xin Yu; Zhi-Yuan Sun; Kai-Wen Zhou; Yu-Jia Shen Pages: 30 - 36 Abstract: Publication date: January 2018 Source:Applied Mathematics Letters, Volume 75 Author(s): Xin Yu, Zhi-Yuan Sun, Kai-Wen Zhou, Yu-Jia Shen A variable-coefficient forced Korteweg–de Vries equation with spacial inhomogeneity is investigated in this paper. Under constraints, this equation is transformed into its bilinear form, and multi-soliton solutions are derived. Effects of spacial inhomogeneity for soliton velocity, width and background are discussed. Nonlinear tunneling for this equation is presented, where the soliton amplitude can be amplified or compressed. Our results might be useful for the relevant problems in fluids and plasmas.

Authors:Chenyin Qian Pages: 37 - 42 Abstract: Publication date: January 2018 Source:Applied Mathematics Letters, Volume 75 Author(s): Chenyin Qian We consider the Prodi–Serrin type regularity criterion involving ∂ 3 u h and the third component of velocity (or the gradient of velocity). In particular, if the ∂ 3 u h satisfies the end-point Prodi–Serrin type condition, one can show that Leray’s weak solutions of the three-dimensional Navier–Stokes equations become regular with the help of additional assumption on the third component of velocity (or the gradient of velocity field).

Authors:Eugenio Aulisa; Sara Calandrini; Giacomo Capodaglio Pages: 43 - 49 Abstract: Publication date: January 2018 Source:Applied Mathematics Letters, Volume 75 Author(s): Eugenio Aulisa, Sara Calandrini, Giacomo Capodaglio We present sufficient conditions for field-of-values-equivalence between block triangular preconditioners and generalized saddle-point matrices arising from inf–sup stable finite element discretizations. We generalize a result by Loghin and Wathen (2004) for matrices with a pure saddle-point structure to the case where the ( 2 , 2 ) block is non-zero. Moreover, we extend the analysis to the case where the ( 2 , 1 ) block is not the transpose of the ( 1 , 2 ) block.

Authors:J.A. Ezquerro; M.A. Hernández-Verón Pages: 50 - 58 Abstract: Publication date: January 2018 Source:Applied Mathematics Letters, Volume 75 Author(s): J.A. Ezquerro, M.A. Hernández-Verón We use the majorant principle of Kantorovich to analyze the semilocal convergence of Newton’s method when it is applied to some Hammerstein integral equations. Moreover, from using the theoretical significance of the result obtained, we draw conclusions about the existence and uniqueness of solution of the equations. Furthermore, a solution of a Hammerstein integral equation with non-separable kernel is approximated.

Authors:Carla Baroncini; Julián Fernández Bonder; Juan F. Spedaletti Pages: 59 - 67 Abstract: Publication date: January 2018 Source:Applied Mathematics Letters, Volume 75 Author(s): Carla Baroncini, Julián Fernández Bonder, Juan F. Spedaletti In this paper, we give sufficient conditions on the approximating domains in order to obtain the continuity of solutions for the fractional p -Laplacian. These conditions are given in terms of the fractional capacity of the approximating domains.

Authors:Guodong Wang; Yanbo Hu Pages: 68 - 73 Abstract: Publication date: January 2018 Source:Applied Mathematics Letters, Volume 75 Author(s): Guodong Wang, Yanbo Hu We consider the scalar conservation laws with discontinuous flux function ( 1 − H ( x ) ) g ( u ) + H ( x ) f ( u ) , where f and g are smooth nonlinear functions, and H ( x ) is the Heaviside function. By entropy solutions of type ( A , B ) , which is defined by Bürger et al. (2009), we introduce a simple and efficient Roe-type interface flux, which is Lipschitz continuous and monotone. Riemann solvers are not involved at the interface x = 0 . In addition, some numerical results are presented to demonstrate the behavior of this interface flux.

Authors:Lei Du; Tomohiro Sogabe; Shao-Liang Zhang Pages: 74 - 81 Abstract: Publication date: January 2018 Source:Applied Mathematics Letters, Volume 75 Author(s): Lei Du, Tomohiro Sogabe, Shao-Liang Zhang In this paper, we consider the solution of tridiagonal quasi-Toeplitz linear systems. By exploiting the special quasi-Toeplitz structure, we give a new decomposition form of the coefficient matrix. Based on this matrix decomposition form and combined with the Sherman–Morrison formula, we propose an efficient algorithm for solving the tridiagonal quasi-Toeplitz linear systems. Although our algorithm takes more floating-point operations (FLOPS) than the L U decomposition method, it needs less memory storage and data transmission and is about twice faster than the L U decomposition method. Numerical examples are given to illustrate the efficiency of our algorithm.

Authors:Kui Chen; Da-jun Zhang Pages: 82 - 88 Abstract: Publication date: January 2018 Source:Applied Mathematics Letters, Volume 75 Author(s): Kui Chen, Da-jun Zhang In this letter we propose an approach to obtain solutions for the nonlocal nonlinear Schrödinger hierarchy from the known ones of the Ablowitz–Kaup–Newell–Segur hierarchy by reduction. These solutions are presented in terms of double Wronskian and some of them are new. The approach is general and can be used for other systems with double Wronskian solutions which admit local and nonlocal reductions.

Authors:Xiaoliang Zhou; Wu-Sheng Wang; Ruyun Chen Pages: 89 - 95 Abstract: Publication date: January 2018 Source:Applied Mathematics Letters, Volume 75 Author(s): Xiaoliang Zhou, Wu-Sheng Wang, Ruyun Chen In this paper, the interval qualitative properties of a class of mixed nonlinear impulsive differential equations are studied. Under the hypothesis of delay σ ( t ) being variable, the ratio of functions x ( t − σ ( t ) ) and x ( t ) on each considered interval is estimated, then Riccati transformation and \omega functions are applied to obtain interval oscillation criteria. The results gained by Özbekler and Zafer (2011) for delay σ ( t ) = 0 and by Guo et al. (2012) for delay σ ( t ) being nonnegative constant are developed.

Authors:Wei Wang; Wanbiao Ma Pages: 96 - 101 Abstract: Publication date: January 2018 Source:Applied Mathematics Letters, Volume 75 Author(s): Wei Wang, Wanbiao Ma A diffusive HIV infection model with nonlocal delayed transmission is proposed. In a bounded spatial domain, we investigate threshold dynamics in terms of basic reproduction number ℛ 0 for the heterogeneous model.

Authors:Mingxin Wang Pages: 102 - 107 Abstract: Publication date: January 2018 Source:Applied Mathematics Letters, Volume 75 Author(s): Mingxin Wang In this note we introduce a direct approach for the Lyapunov functional method to study the global stability of the unique equilibrium solution of reaction diffusion systems and partially degenerate reaction diffusion systems permitting with delays. We first provide the abstract framework and results. Then we give an example as the application.

Authors:Harsha Hutridurga; Francesco Salvarani Pages: 108 - 113 Abstract: Publication date: January 2018 Source:Applied Mathematics Letters, Volume 75 Author(s): Harsha Hutridurga, Francesco Salvarani In this article we prove local-in-time existence and uniqueness of solution to a non-isothermal cross-diffusion system with Maxwell–Stefan structure.

Authors:Xiao-Juan Zhao; Rui Guo; Hui-Qin Hao Pages: 114 - 120 Abstract: Publication date: January 2018 Source:Applied Mathematics Letters, Volume 75 Author(s): Xiao-Juan Zhao, Rui Guo, Hui-Qin Hao In this paper, a discrete Hirota equation is analytically investigated. The N -fold Darboux transformation (DT) is constructed based on the Lax pair for the equation. In addition, the discrete N -soliton solutions under the vanishing background are derived. Especially, the dynamic features of one-soliton and two-soliton solutions are displayed through figures.

Authors:M. Chhetri; P. Girg Pages: 121 - 127 Abstract: Publication date: January 2018 Source:Applied Mathematics Letters, Volume 75 Author(s): M. Chhetri, P. Girg We consider a system of the form − Δ u = λ g 1 ( x , u , v ) in Ω ; − Δ v = λ g 2 ( x , u , v ) in Ω ; u = 0 = v on ∂ Ω , where λ > 0 is a parameter, Ω ⊂ R N ( N ≥ 2 ) is a bounded domain with sufficiently smooth boundary ∂ Ω (a bounded open interval if N = 1 ). Here g i ( x , s , t ) : Ω × [ 0 , + ∞ ) × [ 0 , + ∞ ) → R ( i = 1 , 2 ) are Carathéodory functions that exhibit superlinear growth at infinity involving product of powers of u and v . Using re-scaling argument combined with Leray–Schauder degree theory and a version of Leray–Schauder continuation theorem, we show that the system has a connected set of positive solutions for λ small.

Authors:Sun Hye Park Pages: 128 - 134 Abstract: Publication date: January 2018 Source:Applied Mathematics Letters, Volume 75 Author(s): Sun Hye Park In this paper we consider a von Karman equation with time delay. Many researchers have studied well-posedness, decay rates of energy, and existence of attractors for von Karman equations without delay effects. But there are few works on von Karman equations with time delay. Moreover there are not many studies on attractors for other delayed systems. Thus, we discuss the existence of global attractors for the von Karman equation with time delay by establishing energy functionals which are related to the norm of the phase space to our problem.

Authors:Qian-Min Huang; Yi-Tian Gao; Lei Hu Pages: 135 - 140 Abstract: Publication date: January 2018 Source:Applied Mathematics Letters, Volume 75 Author(s): Qian-Min Huang, Yi-Tian Gao, Lei Hu In this letter, breather-to-soliton transition is studied for an integrable sixth-order nonlinear Schrödinger equation in an optical fiber. Constraint for the breather-to-soliton transition is given. Breathers could be transformed into the different types of solitons, which are determined by the values of the real and imaginary parts of the eigenvalues in the Darboux transformation. Interactions of the breathers and breathers, of the breathers and solitons, as well as of the solitons and solitons, are graphically presented.

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.

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.

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.

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.

Authors:Guo Lin Abstract: Publication date: February 2018 Source:Applied Mathematics Letters, Volume 76 Author(s): Guo Lin This paper is concerned with the minimal wave speed of competitive diffusive systems, of which the corresponding wave system is of infinite dimensional. By constructing upper and lower solutions, the existence of traveling wave solutions is confirmed, which shows the minimal wave speed. Therefore, it completes the known results.

Authors:Xian Abstract: Publication date: February 2018 Source:Applied Mathematics Letters, Volume 76 Author(s): Ke Wu, Xian Wu We consider the existence of radial solutions for the quasilinear Schrödinger equation − △ u + V ( x ) u − κ u △ u 2 = u p − 2 u , x ∈ R N . where κ > 0 , N ≥ 3 , 2 < p < 2 2 ∗ and V ∈ C 1 ( R ) . Here we are interested in the case that 2 < p ≤ 4 since the existence of solutions for 4 < p < 2 2 ∗ can be easily obtained by a standard variational argument. Our method is based on the Pohožaev type identity.