具连续分布滞量的中立型向量抛物偏泛函微分方程的H-振动性

研究一类具连续分布滞量的中立型向量抛物偏泛函微分方程的H-振动性,利用向量的内积和Green公式,获得了该类方程在Dirichlet边值条件下所有解H-振动的充分判据,这里H是Rm中的单位向量.     

脉冲中向量中立型抛物偏微分方程的H-振动性

研究一类脉冲向量中立型抛物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中立型微分不等式不存在最终正解的问题,建立了该类方程在Dirichlet边值条件下所有解H-振动的若干充分判据,这里H是R~M中的单位向量.     

中立型向量双曲偏微分方程的H-振动性

本文研究了一类中立型向量双曲偏微分方程边值问题的振动性.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泛函微分不等式正解的不存在性问题,获得了该类边值问题在Dirichlet边界条件下所有解H-振动的若干新的充分条件,其中H是Rm中的单位向量.     

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.     

具连续分布滞量的非线性中立型抛物偏泛函微分方程的振动性

考虑一类具连续分布滞量的非线性中立型抛物偏泛函微分方程解的振动性,借助Green定理和时滞微分不等式获得了这类方程在Robin,Dirichlet边值条件下所有解振动的若干充分条件.     

一类具分布式偏差变元的双曲型向量泛函微分方程解的H-振动性

研究了一类具有分布式偏差变元的中立型向量双曲泛函微分方程解的H-振动性.给出了判别解的H-振动性的一些充分条件.     

中立抛物型偏微分方程解的强迫振动

本讨论一类多滞量中立抛物型偏微分方程解的振动性物,获得了其一切解振动的充分条件,指出了与普通抛物型偏微分方程质的差异。     

具有分布偏差变元的偶数阶中立型阻尼泛函微分方程的振动准则

考虑一类具有分布偏差变元的偶数阶中立型阻尼泛函微分方程的振动性,利用积分平均技巧和Riccati变换,获得了该类方程振动的几个准则,推广了现有文献的一些结果,并给出了几个应用实例.     

非线性中立型抛物微分方程解的振动性

This paper deals with the oscillatory properties of a class of nonlinear neutral parabolic partial differential equations with several delays. Sufficient criteria for the equation to be oscillatory are obtained by making use of some results of first-order functional differential inequalities. These results fully reveal the essential difference between this type and that without delays.     

一类具偏差变元非线性偏微分方程解的振动性

研究了一类具有偏差变元的非线性偏微分方程解的振动性，获得了方程所有解振动的充分条件。     

Stability analysis of parabolic partial differential equations with piecewise continuous arguments

This article deals with the analytic and numerical stability of numerical methods for a parabolic partial differential equation with piecewise continuous arguments of alternately retarded and advanced type. First, application of the theory of separation of variables in matrix form and the Fourier method, the necessary and sufficient condition under which the analytic solution is asymptotically stable is derived. Then, the θ‐methods are applied to solve the corresponding initial value problem, the sufficient conditions for the asymptotic stability of numerical methods are obtained. Finally, several numerical examples are presented to support the theoretical results. © 2016 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 531–545, 2017     

Global attractivity of periodic solution for neutral functional differential system with multiple deviating arguments

In this paper, a kind of neutral functional differential system with multiple deviating arguments is considered. By means of Mawhin's coincidence degree theory and Lyapunov method, a sufficient condition is obtained for guaranteeing the existence and global attractivity of periodic solution for the system. It is interesting that the result is related to the multiple deviating arguments τ_i(i = 1, 2, …, m). An example is given to show the feasibility of the result in the last section. Copyright © 2011 John Wiley & Sons, Ltd.     

具偏差变元的中立型微分方程正周期解的存在性

By means of an abstract continuation theorem, the existence criteria are established for the positive periodic solutions of a neutral functional differential equation dN/dt=N(t)[a(t)-β(t)N(t)-b(t)N(t-a(t))-c(t)N(t-τ(t))]     

Oscillation for systems of nonlinear neutral type parabolic partial functional differential equations

This paper discusses the oscillation of solutions for systems of nonlinear neutral type parabolic partial fuctional differential equations of the form     

On the forced oscillation of systems of neutral parabolic differential equations with deviating arguments

Sufficient conditions are established for the forced oscillation of systems of neutral parabolic differential equations with deviating arguments. The main results are illustrated by some examples.     

二阶中立型微分方程的振动准则

研究了一类具有连续偏差变元的二阶非线性中立型方程,得到了该类方程的振动准则     

The existence of periodic solutions for three-order neutral differential equations

In this paper, by using Kranoselskii fixed point point theorem and Mawhin''s continuation theorem, we establish two existence theorem on the periodic solutions for a class of three-order neutral differential equations.     

Degenerate parabolic stochastic partial differential equations

We study the Cauchy problem for a scalar semilinear degenerate parabolic partial differential equation with stochastic forcing. In particular, we are concerned with the well-posedness in any space dimension. We adapt the notion of kinetic solution which is well suited for degenerate parabolic problems and supplies a good technical framework to prove the comparison principle. The proof of existence is based on the vanishing viscosity method: the solution is obtained by a compactness argument as the limit of solutions of nondegenerate approximations.     

On the oscillation of solutions of first order differential equations with deviating arguments

1.IntroductionConsiderthefirstorderdifferentialequationwithdeviatingargUmelltTheoscillationofEq.(1)wasstudiedextensivelyinthelastthreedecades.See,forexamDleif--101andthereferencescitedtherein.In1972Ladas.LakshlnhanthamanddeceivedApril1,1997.Re~AugUBt...