脉冲向量时滞抛物型方程的H-振动性

研究一类脉冲向量时滞抛物型偏微分方程的振动性,借助Domslak引进的H-振动的概念及内积降维的方法,将多维振动问题化为一维脉冲时滞微分不等式不存在最终正解的问题,建立了该类方程在Robin边值条件下所有解H-振动的若干充分条件,这里H是RM中的单位向量.     

带脉冲和时滞影响的非线性双曲型方程振动性的新准则

考虑一类具非线性扩散项的脉冲时滞双曲型偏微分方程的振动性,借助一阶脉冲时滞微分不等式,获得了该类方程在Dirichlet边值条件下所有解振动的若干充分判据.     

一类脉冲时滞双曲型方程组解的振动性

本文研究含脉冲的时滞双曲型方程组解的振动性,利用二阶脉冲微分不等式的性质,得到了方程组在两类不同边界条件下解振动的一些充分判据.     

具有脉冲扰动的非线性时滞微分方程

本文研究一类脉冲非线性时滞微分方程解的性质，讨论了其解的整体存在性及非振动解的渐近性，也给出了其所有解振动的充分条件．     

脉冲时滞抛物型偏微分方程组解的振动性

研究一类脉冲时滞抛物型偏微分方程组解的振动性,利用一阶脉冲时滞微分不等式获得了该类方程组在两类不同边值条件下所有解振动的若干充分条件.所得结果充分反映了脉冲和时滞在振动中的影响作用.     

非线性脉冲向量双曲型微分方程解的H-振动性

研究一类具脉冲时滞的非线性双曲型向量泛函微分方程解的H-振动性.方法是采用由Domslak引进的H-振动性的概念,将向量微分方程解的振动问题转化为纯量微分不等式正解和负解的不存在性问题.得到了解的H-振动性的若干判别准则.     

具高阶Laplace算子的非线性脉冲时滞双曲型方程的振动性

研究一类具高阶Laplace算子的非线性脉冲时滞双曲型偏泛函微分方程,利用二阶脉冲时滞微分不等式,得到了该类方程在两类不同边值条件下所有有界解振动的若干充分判据.     

一类二阶非线性脉冲时滞微分方程的振动性

考虑一类二阶非线性脉冲时滞微分方程,得到了方程所有解振动的两个充分条件,推广了D■urina和Stavroulakis[Appl Math Comput,2003,140,445—453]中关于非脉冲方程的相关结果.     

非线性中立抛物型偏微分方程系统的振动性定理

研究一类非线性中立抛物型时滞偏微分方程系统解的振动性质,利用积分不等式和泛函微分方程的某些结果,获得了该类系统在第一类边值条件下所有解振动的若干充分条件.结论充分表明振动是由时滞量引起的.     

脉冲向量中立型抛物方程解的H-振动性

研究一类脉冲向量中立型抛物偏微分方程边值问题解的振动性,利用Domslak引进的H-振动的概念及内积降维的方法,将多维振动问题化为一维脉冲中立型微分不等式正解的不存在性问题,并借助于一阶脉冲中立型微分不等式,给出了该类边值问题所有解H-振动的若干充分性判据,这里H是R~M中的单位向量.     

New exact solutions to breaking soliton equations and Whitham-Broer-Kaup equations

In this paper, by using the improved Riccati equations method, we obtain several types of exact traveling wave solutions of breaking soliton equations and Whitham-Broer-Kaup equations. These explicit exact solutions contain solitary wave solutions, periodic wave solutions and the combined formal solitary wave solutions. The method employed here can also be applied to solve more nonlinear evolution equations.     

Prolongation of solutions of measure differential equations and dynamic equations on time scales

In this paper, we prove the results on existence and uniqueness of the maximal solutions for measure differential equations, considering more general conditions on functions f and g by using the correspondence between the solutions of these equations and the solutions of generalized ODEs. Moreover, we prove these results for the dynamic equations on time scales, using the correspondence between the solutions of these last equations and the solutions of the measure differential equations.     

Oscillation of solutions of second-order linear differential equations and corresponding difference equations

In this paper, we present conditions ensuring that solutions of linear second-order differential equations oscillate, provided solutions of corresponding difference equations oscillate. We also establish the converse result, namely, when oscillation of solutions of difference equations implies oscillation of solutions of corresponding differential equations.     

On Gaussian decay estimates of solutions to some linear elliptic equations and their applications

In this paper we establish pointwise decay estimates of solutions to some linear elliptic equations by using the Nash–Moser iteration arguments and the ODE method. As applications we obtain sharp Gaussian decay estimates for solutions to nonlinear elliptic equations that are related with self-similar solutions to nonlinear heat equations and standing wave solutions to nonlinear Schrödinger equations with harmonic potential.     

An application of the decomposition method for the generalized KdV and RLW equations

We consider solitary-wave solutions of the generalized regularized long-wave (RLW) and Korteweg-de Vries (KdV) equations. We prove the convergence of Adomian decomposition method applied to the generalized RLW and KdV equations. Then we obtain the exact solitary-wave solutions and numerical solutions of the generalized RLW and KdV equations for the initial conditions. The numerical solutions are compared with the known analytical solutions. Their remarkable accuracy are finally demonstrated for the generalized RLW and KdV equations.     

Complexiton solutions of the Korteweg–de Vries equation with self-consistent sources

Complexiton solutions to the Korteweg–de Vires equation with self-consistent sources are presented. The basic technique adopted is the Darboux transformation. The resulting solutions provide evidence that soliton equations with self-consistent sources can have complexiton solutions, in addition to soliton, positon and negaton solutions. This also implies that soliton equations with self-consistent sources possess some kind of analytical characteristics that linear differential equations possess and brings ideas toward classification of exact explicit solutions of nonlinear integrable differential equations.     

Functional equations with extrema

Exact solutions of sine Gordon and multiple sine Gordon equations are constructed in terms of solutions of a linear base equation, the Klein Gordon equation and also in terms of nonlinear base equations where the nonlinearity is polynomial in the dependent variable. Further, exact solutions of nonlinear generalizations of the Schrodinger equation and of additional nonlinear generalizations of the Klein Gordon equation are constructed in terms of solutions of linear base equations. Finally, solutions with spherical symmetry, of nonlinear Klein Gordon equations are given.     

Nondegeneracy and uniqueness of positive solutions for Robin problem of second order ordinary differential equations and its applications

This article studies positive solutions of Robin problem for semi-linear second order ordinary differential equations. Nondegeneracy and uniqueness results are proven for homogeneous differential equations. Necessary and sufficient conditions for the existence of one or two positive solutions for inhomogeneous differential equations or differential equations with concave-convex nonlinearities are obtained by making use of the nondegeneracy and uniqueness results for positive solutions of homogeneous differential equations.     

Complexiton solutions of the Korteweg–de Vries equation with self-consistent sources

Complexiton solutions to the Korteweg–de Vires equation with self-consistent sources are presented. The basic technique adopted is the Darboux transformation. The resulting solutions provide evidence that soliton equations with self-consistent sources can have complexiton solutions, in addition to soliton, positon and negaton solutions. This also implies that soliton equations with self-consistent sources possess some kind of analytical characteristics that linear differential equations possess and brings ideas toward classification of exact explicit solutions of nonlinear integrable differential equations.     

Approximation of the incompressible convective Brinkman–Forchheimer equations

This paper studies the approximation of solutions for the incompressible convective Brinkman–Forchheimer (CBF) equations via the artificial compressibility method. We first introduce a family of perturbed compressible CBF equations that approximate the incompressible CBF equations. Then, we prove the existence and convergence of solutions for the compressible CBF equations to the solutions of the incompressible CBF equations.