Authors:A.G. Ramm Pages: 1 - 5 Abstract: Publication date: March 2018 Source:Applied Mathematics Letters, Volume 77 Author(s): A.G. Ramm P. Novikov in 1938 has proved that if u 1 ( x ) = u 2 ( x ) for x > R , where R > 0 is a large number, u j ( x ) ≔ ∫ D j g 0 ( x , y ) d y , g 0 ( x , y ) ≔ 1 4 π x − y , and D j ⊂ R 3 , j = 1 , 2 , D j ⊂ B R , are bounded, connected, smooth domains, star-shaped with respect to a common point, then D 1 = D 2 . Here B R ≔ { x : x ≤ R } . Our basic results are: (a) the removal of the assumption about star-shapeness of D j , (b) a new approach to the problem, (c) the construction of counter-examples for a similar problem in which g 0 is replaced by g = e i k x − y 4 π x − y , where k > 0 is a fixed constant.

Authors:M.J. Park; O.M. Kwon; J.H. Ryu Pages: 6 - 12 Abstract: Publication date: March 2018 Source:Applied Mathematics Letters, Volume 77 Author(s): M.J. Park, O.M. Kwon, J.H. Ryu This paper investigates a stability problem for linear systems with time-delay. By constructing simple Lyapunov–Krasovskii functional (LKF), and utilizing a new generalized integral inequality (GII) proposed in this paper, a sufficient stability condition for the systems will be derived in terms of linear matrix inequalities (LMIs). Two illustrative examples are given to show the superiorities of the proposed criterion.

Authors:Wenjun Cui; Lijia Han Pages: 13 - 20 Abstract: Publication date: March 2018 Source:Applied Mathematics Letters, Volume 77 Author(s): Wenjun Cui, Lijia Han This paper is devoted to the study of the infinite propagation speed and the asymptotic behavior for a generalized Camassa–Holm equation with cubic nonlinearity. First, we get the infinite propagation speed in the sense that the corresponding solution with compactly supported initial data does not have compact support any longer in its lifespan. Then, the asymptotic behavior of the solution at infinity is investigated. Especially, we prove that the solution decays algebraically with the same exponent as that of the initial data.

Authors:Yanbing Yang; Runzhang Xu Pages: 21 - 26 Abstract: Publication date: March 2018 Source:Applied Mathematics Letters, Volume 77 Author(s): Yanbing Yang, Runzhang Xu This paper is concerned with the finite time blow up of the solution to the Cauchy problem for the Klein–Gordon equation at arbitrarily positive initial energy level. By introducing a new auxiliary function and an adapted concavity method we establish some sufficient conditions on initial data such that the solution blows up in finite time, which extends the results established in Wang (2008).

Authors:Zhong Tan; Wenpei Wu; Jianfeng Zhou Pages: 27 - 34 Abstract: Publication date: March 2018 Source:Applied Mathematics Letters, Volume 77 Author(s): Zhong Tan, Wenpei Wu, Jianfeng Zhou In this paper, we consider the incompressible magneto-hydro-dynamic equations in the whole space. We first show that there exist global mild solutions with small initial data in the scaling invariant space. The main technique we have used is implicit function theorem which yields necessarily continuous dependence of solutions for the initial data. Moreover, we gain the asymptotic stability of solutions as the time goes to infinity. Finally, as a byproduct of our construction of solutions in the weak L p -spaces, the existence of self-similar solutions was established provided the initial data are small homogeneous functions.

Authors:Chun Shen Pages: 35 - 43 Abstract: Publication date: March 2018 Source:Applied Mathematics Letters, Volume 77 Author(s): Chun Shen The Riemann solutions for a symmetric Keyfitz–Kranzer system are constructed explicitly, in which some singular hyperbolic waves are discovered such as the delta shock wave and the composite wave J R . The global solutions to the double Riemann problem are achieved when the delta shock wave is involved. It is shown that a delta shock wave is separated into a delta contact discontinuity and a shock wave during the process of constructing solutions.

Authors:Vladimir Mityushev Pages: 44 - 48 Abstract: Publication date: March 2018 Source:Applied Mathematics Letters, Volume 77 Author(s): Vladimir Mityushev Extensions of Maxwell’s self-consistent approach from single- to n - inclusions problems lead to cluster methods applied to computation of the effective properties of composites. We describe applications of Maxwell’s formalism to finite clusters and explain the uncertainty arising when n tends to infinity by study of the corresponding conditionally convergent series.

Authors:F.Z. Geng; S.P. Qian Pages: 49 - 56 Abstract: Publication date: March 2018 Source:Applied Mathematics Letters, Volume 77 Author(s): F.Z. Geng, S.P. Qian Based on the piecewise polynomial reproducing kernels, the authors presented the reproducing kernel method(RKM) for nonlocal boundary value problems. In this paper, we will present an optimal RKM for linear nonlocal boundary value problems by combining the piecewise polynomial kernel with polynomial kernel. The method is of high accuracy. Also, the method can avoid reducing the inhomogeneous boundary conditions to homogeneous boundary conditions and constructing reproducing kernel satisfying corresponding homogeneous boundary conditions. Numerical examples are included to demonstrate the validity of the new method.

Authors:Shaoqin Gao; Zimeng Chen; Wenying Shi Pages: 64 - 71 Abstract: Publication date: March 2018 Source:Applied Mathematics Letters, Volume 77 Author(s): Shaoqin Gao, Zimeng Chen, Wenying Shi In this paper, we establish some new criteria for oscillation and asymptotic behavior of solutions of a certain class of third-order neutral differential equations with continuously distributed delay. We study the case of noncanonical equations subject to various conditions. An example is given to illustrate the main results.

Authors:Chengbin Liang; JinRong Wang; D. O’Regan Pages: 72 - 78 Abstract: Publication date: March 2018 Source:Applied Mathematics Letters, Volume 77 Author(s): Chengbin Liang, JinRong Wang, D. O’Regan This paper gives a representation of a solution to the Cauchy problem for a fractional linear system with pure delay. We introduce the fractional delayed matrices cosine and sine of a polynomial of degree and establish some properties. Then, we use the variation of constants method to obtain the solution and our results extend those for second order linear system with pure delay. As an application, the representation of a solution is used to obtain a finite time stability result.

Authors:Vitaly Katsnelson; Linh V. Nguyen Pages: 79 - 86 Abstract: Publication date: March 2018 Source:Applied Mathematics Letters, Volume 77 Author(s): Vitaly Katsnelson, Linh V. Nguyen In this article, we consider the inverse source problem arising in thermo/photo-acoustic tomography in elastic media. We show that the time reversal method, proposed by Tittelfitz (2012), converges with the sharp observation time without any constraint on the speeds of the longitudinal and shear waves.

Authors:Nikolaos S. Papageorgiou; Vicenţiu D. Rădulescu; Dušan D. Repovš Pages: 87 - 93 Abstract: Publication date: March 2018 Source:Applied Mathematics Letters, Volume 77 Author(s): Nikolaos S. Papageorgiou, Vicenţiu D. Rădulescu, Dušan D. Repovš We study a semilinear parametric elliptic equation with superdiffusive reaction and mixed boundary conditions. Using variational methods, together with suitable truncation techniques, we prove a bifurcation-type theorem describing the nonexistence, existence and multiplicity of positive solutions.

Authors:Xinwei Wang Pages: 94 - 100 Abstract: Publication date: March 2018 Source:Applied Mathematics Letters, Volume 77 Author(s): Xinwei Wang A novel differential quadrature element method is presented for free vibration analysis of hybrid nonlocal Euler–Bernoulli beams with any combination of boundary conditions. Explicit formulas of computing the weighting coefficients of various derivatives are derived. Sixth-order differential equations are successfully solved by using the proposed method. Accurate frequencies are obtained and presented. The proposed method can be also used for accurate solutions of various sixth-order differential equations and beam structures with minimum computational effort.

Authors:Aiyong Chen; Caixing Tian; Wentao Huang Pages: 101 - 107 Abstract: Publication date: March 2018 Source:Applied Mathematics Letters, Volume 77 Author(s): Aiyong Chen, Caixing Tian, Wentao Huang In this letter, we study the periodic solutions of the equation of barotropic Friedmann–Robertson–Walker cosmologies. Using variable transformation, the original second order ordinary differential equation is converted to a planar dynamical system. We prove that the planar dynamical system has two isochronous centers under certain parameter conditions by using Picard–Fuchs equation. Consequently, we find that there exist two families of periodic solutions with equal period for the Friedmann–Robertson–Walker model.

Authors:Wenping Fan; Fawang Liu Pages: 114 - 121 Abstract: Publication date: March 2018 Source:Applied Mathematics Letters, Volume 77 Author(s): Wenping Fan, Fawang Liu In this paper, the two-dimensional distributed order space-fractional diffusion equation on an irregular convex domain is considered. The finite element method using unstructured mesh adapted to the irregular domain is proposed to solve the considered equation. To testify the efficiency of the proposed method, two numerical examples are given. By the error analysis and the comparison between the numerical solution and the exact solution, the finite element method applied in this paper is shown to be valid in solving the two-dimensional distributed order space-fractional diffusion equation on an irregular convex domain.

Authors:Sa Jun Park; Seok-Bae Yun Pages: 122 - 129 Abstract: Publication date: March 2018 Source:Applied Mathematics Letters, Volume 77 Author(s): Sa Jun Park, Seok-Bae Yun In this paper, we show that the entropy production functional for the polyatomic ellipsoidal BGK model can be decomposed into two non-negative parts. Two applications of this property: the H -theorem for the polyatomic BGK model and the weak compactness of the polyatomic ellipsoidal relaxation operator, are discussed.

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:Qiaozhen Zhu; Jian Xu; Engui Fan Pages: 81 - 89 Abstract: Publication date: February 2018 Source:Applied Mathematics Letters, Volume 76 Author(s): Qiaozhen Zhu, Jian Xu, Engui Fan We present a Riemann–Hilbert problem formalism for the initial value problem of the Kundu–Eckhaus equation on the line. The long-time asymptotic for the solutions of the Kundu–Eckhaus equation is further analyzed via the Deift–Zhou nonlinear steepest descent method.

Authors:Zhipeng Yang; Fukun Zhao Pages: 90 - 95 Abstract: Publication date: February 2018 Source:Applied Mathematics Letters, Volume 76 Author(s): Zhipeng Yang, Fukun Zhao In this paper, we study the following fractional Schrödinger equation ( − Δ ) s u + V ( x ) u = K ( x ) f ( u ) + λ W ( x ) u p − 2 u , x ∈ R N , where λ > 0 is a parameter, ( − Δ ) s denotes the fractional Laplacian of order s ∈ ( 0 , 1 ) , N > 2 s , W ∈ L 2 2 − p ( R N , R + ) , 1 < p < 2 , V , K are nonnegative continuous functions and f is a continuous function with a quasicritical growth. Under some mild assumptions, we prove that the above equation has three solutions.

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:Hai-Qiang Zhang; Meng-Yue Zhang; Rui Hu Pages: 170 - 174 Abstract: Publication date: February 2018 Source:Applied Mathematics Letters, Volume 76 Author(s): Hai-Qiang Zhang, Meng-Yue Zhang, Rui Hu In this Letter, we study a nonlocal vector nonlinear Schrödinger (NVNLS) equation with self-induced parity-time-symmetric potential. We construct the N -fold Darboux transformation in terms of compact determinant forms. Starting from the non-vanishing background, we give the general solution of spectral problem, which allows us to derive many different types of exact analytical solutions of the NVNLS equation, like the breathers, dark and anti-dark solitons. With three-component case as an example, we display three types of two-soliton elastic collision behaviors: breather and dark soliton, breather and anti-dark soliton, dark soliton and anti-dark soliton.

Authors:Huajun Gong; Xian-gao Liu; Xiaotao Zhang Pages: 175 - 180 Abstract: Publication date: February 2018 Source:Applied Mathematics Letters, Volume 76 Author(s): Huajun Gong, Xian-gao Liu, Xiaotao Zhang In this article, we study the steady-state solutions of the coupled Navier–Stokes and Q-tensor system in R d . We proved the Liouville theorem that u = 0 , Q = 0 with the conditions u ∈ L 3 d d − 1 ( R d ) ∩ H ̇ 1 ( R d ) , Q ∈ H 2 ( R d ) and b 2 − 24 a c ≤ 0 ( d = 2 , 3 ).

Authors:Weihua Wang; Gang Wu Pages: 181 - 186 Abstract: Publication date: February 2018 Source:Applied Mathematics Letters, Volume 76 Author(s): Weihua Wang, Gang Wu In this paper, we establish the global well-posedness of mild solution to the three-dimensional incompressible generalized Navier–Stokes equations with Coriolis force if the initial data are in X 1 − 2 α defined by X 1 − 2 α = { u ∈ D ′ ( R 3 ) : ∫ R 3 ξ 1 − 2 α u ˆ ( ξ ) d ξ < + ∞ } . In addition, we also give Gevrey class regularity of the solution.

Authors:Dragos-Patru Covei Pages: 187 - 194 Abstract: Publication date: February 2018 Source:Applied Mathematics Letters, Volume 76 Author(s): Dragos-Patru Covei In this paper, we provide sufficient conditions for the boundedness and unboundedness of the entire solutions for a semilinear elliptic system of the following type Δ u = p 1 x f u , v , x ∈ R N , Δ v = p 2 x g u , x ∈ R N , N ≥ 3 . Here p 1 , f , p 2 and g are continuous functions satisfying certain properties. Furthermore, we study the case where the system is not of a variational type. Our results are obtained by a straightforward application of the Arzela–Ascoli theorem.

Authors:Shi-Liang Wu; Cui-Xia Li Pages: 195 - 200 Abstract: Publication date: February 2018 Source:Applied Mathematics Letters, Volume 76 Author(s): Shi-Liang Wu, Cui-Xia Li In this paper, we focus on the unique solution of the absolute value equations (AVE). Using an equivalence relation to the linear complementarity problem (LCP), two necessary and sufficient conditions for the unique solution of the AVE are presented. Based on the obtained results, some new sufficient conditions for the unique solution of the AVE are obtained.

Authors:Kai Liu Abstract: Publication date: March 2018 Source:Applied Mathematics Letters, Volume 77 Author(s): Kai Liu In this work, we establish a theory about the almost sure pathwise exponential stability property for a class of stochastic neutral functional differential equations by developing a semigroup scheme for the drift part of the systems under consideration and dealing with their pathwise stability through a perturbation approach, rather than through that one to get their moment stability first. As an illustration, we can show that some stochastic systems have their almost sure exponential stability not sensitive to small delays.

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.