Boundary Value Problems for Ordinary Differential Equations with Deviated Arguments

We discuss differential equations with nonlinear boundary conditions. We formulate sufficient conditions under which problems with deviating arguments have quasisolutions or solutions. To obtain the results, we apply the method of monotone iterations.     

Controllability of Functional Integro-Differential Inclusions with an Unbounded Delay

In this paper, a sufficient condition is established for the controllability of neutral functional integro-differential inclusions with an unbounded delay in Banach spaces. The approach used is a fixed-point theorem for condensing maps due to Martelli and the theory of analytic semigroup of linear operators. Communicated by F. Zirilli Research supported by NNSF of China, by the Teaching and Research Award Program for Outstanding Young Teachers in Higher Education Institutions of the Ministry of Education of China, and by the Qing Lan Talent Engineering Fund QL-05-164 of Lanzhou Jiaotong University. The authors are grateful to Professor F. Zirilli and two anonymous referees for valuable suggestions improving this paper.     

Asymptotic behavior of solutions for a class of predator-prey reaction-diffusion systems with time delays

The aim of this paper is to investigate the asymptotic behavior of solutions for a class of three-species predator-prey reaction-diffusion systems with time delays under homogeneous Neumann boundary condition. Some simple and easily verifiable conditions are given to the rate constants of the reaction functions to ensure the convergence of the time-dependent solution to a constant steady-state solution. The conditions for the convergence are independent of diffusion coefficients and time delays, and the conclusions are directly applicable to the corresponding parabolic-ordinary differential system and to the corresponding system without time delays.     

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.     

OSCILLATION FOR NONAUTONOMOUS NEUTRAL DYNAMIC DELAY EQUATIONS ON TIME SCALES

The article is concerned with oscillation of nonautonomous neutral dynamic delay equations on time scales. Sufficient conditions are established for the existence of bounded positive solutions and for oscillation of all solutions of this equation. Some results extend known results for difference equations when the time scale is the set Z of positive integers and for differential equations when the time scale is the set R of real numbers.     

STABILITY AND BOUNDEDNESS OF SOLUTIONS OF VOLTERRA INTEGRAL DIFFERENTIAL EQUATIONS WITH INFINITE DELAY

This paper studies the stability and boundedness of the solutions of Volterra integral differential equations with infinite delay in the phase space (Ch, |·|h), the h-uniform stability, h-uniformly asymptotic stability and h-boundedness of solutions are obtained.     

具非线性中立项的二阶时滞微分方程的振动性质

By using the averaging technique, we obtain new oscillation criteria for second order delay differential equation with nonlinear neutral term. These results generalize and improve some known results about neutral delay differential equation of second order.     

变时滞Hopfield神经网络的全局吸引性和全局指数稳定性

对一类具时滞的Hopfeild型神经网络模型,在非线性神经元激励函数只要求满足Lipschitz连续的条件下,利用推广的Halanay时延微分析不等式、Dini导数以及泛函微分析技术,给出了这类模型的平衡点全局指数稳定性和全局吸引性的充分条件,这些条件易于检验,且改进和推广了前人的结论.此外,此文给出了研究神经网络模型的全局吸引性的微分不等式比较方法.     

非自治时滞微分方程的正周期解

By utilizing a fixed point theorem on cone,some new results on the existence of positive periodic solutions for nonautonomous differential equations with delay are derived.     

一类具有阶段结构和时滞的捕食系统的持续生存和稳定性

我们提出和研究一类带有阶段结构和时滞的捕食模型,得到了种群持续生存的充分条件.研究了阶段结构和时滞对系统稳定性的影响,获得了系统发生Hopf分支和稳定性的条件以及轨道渐进稳定的周期解的存在性.