非自治中立型无穷时滞泛函微分方程的加权伪概自守解

首先引入h型Stepanov 加权伪概自守函数和∞型Stepanov加权伪概自守函数的概念, 接着建立了其函数空间的完备性以及相应组合定理, 最后证明了一类非自治无穷时滞偏中立型泛函微分方程在S^p-加权伪概自守系数下加权伪概自守解的存在唯一性.     

On almost periodic solutions of logistic delay differential equations with almost periodic time dependence

In this paper, we study almost periodic logistic delay differential equations. The existence and module of almost periodic solutions are investigated. In particular, we extend some results of Seifert in [G. Seifert, Almost periodic solutions of certain differential equations with piecewise constant delays and almost periodic time dependence, J. Differential Equations 164 (2000) 451–458].     

具无穷时滞高阶中立型微分方程的周期解

利用重合度理论研究了一类具有无穷时滞高阶中立型泛函微分方程周期解的存在性,获得了该方程存在周期解的充分条件,推广和改进了二阶方程的相应结果.     

具无穷时滞中立型高维非线性系统的周期解

通过构造算子利用Krasnoselskii不动点定理和线性系统的指数二分性讨论了一类具有无穷时滞非线性中立型高维周期微分系统的周期解存在性问题．得到保证系统存在周期解的新的充分条件．     

Asymptotically almost periodic solutions of stochastic functional differential equations

In this paper, we investigate a class of stochastic functional differential equations of the form

dx(t)=(Ax(t)+F(t,x(t),x_t))dt+G(t,x(t),x_t)°dW(t).     

具无穷时滞的中立型Volterra积分微分方程的概周期解

研究了一类具无穷时滞的中立型Volterra积分微分方程的概周期解问题．利用线性系统指数型二分性理论和泛函分析方法,得到了一些关于该方程的概周期解的存在性、唯一性与稳定性的新结果,推广了相关文献的主要结果．     

Existence of almost periodic solutions of second order neutral delay differential equations with piecewise constant argument

By constructing almost periodic sequence solutions to difference equations, the existence of almost periodic solutions of neutral delay differential equations with piecewise constant argument

Existence and uniqueness of solutions to neutral stochastic functional differential equations with infinite delay

This paper investigates the existence and uniqueness theorem of solutions to neutral stochastic differential equations with infinite delay (short for INSFDEs) at a space BC((-∞,0];R^d). Under the uniform Lipschitz condition, linear growth condition is weaken to obtain the moment estimate of the solution for INSFDEs. Furthermore, the existence, uniqueness theorem of the solution for INSFDEs is derived, and the estimate for the error between approximate solution and exact solution is given. On the other hand, under the linear growth condition, the uniform Lipschitz condition is replaced by the local Lipschitz condition, the existence, uniqueness theorem is also valid for INSFDEs on [t₀,T]. Moreover, the existence, uniqueness theorem still holds on interval [t₀,∞), where t₀∈R is an arbitrary real number.     

Periodic solutions of abstract functional differential equations with state‐dependent delay

In this paper, we are concerned with the existence of solutions of systems determined by abstract functional differential equations with infinite and state‐dependent delay. We establish the existence of mild solutions and the existence of periodic solutions. Our results are based on local Lipschitz conditions of the involved functions. We apply our results to study the existence of periodic solutions of a partial differential equation with infinite and state‐dependent delay. Copyright © 2016 John Wiley & Sons, Ltd.     

A new almost periodic type of solutions of second order neutral delay differential equations with piecewise constant argument

A definition of pseudo almost periodic sequence is given and the existence of pseudo almost periodic sequence to difference equation is studied. Based on these, the existence of pseudo almost periodic solutions to neutral delay differential equations with piecewise constant argument is investigated     

On the stability problem for functional differential equations with infinite delay

We study the stability of functional differential equations with infinite delay, using the Lyapunov functional of constant sign with a derivative of constant sign. Limit equations are constructed in a special phase space. We establish a theorem on localization of a positive limit set and theorems on the stability and the asymptotic stability. The results are illustrated by examples.     

On almost periodic mild solutions for stochastic functional differential equations

In this paper, a class of stochastic functional differential equations given by

     

Pseudo almost periodic solutions of differential equations with piecewise constant arguments

In this paper, we give a definition of pseudo almost periodic sequence and study the existence of pseudo almost periodic sequence to difference equation. Based on these, we investigate the existence of pseudo almost periodic solutions to differential equations with piecewise constant arguments which was considered by K. L. Cooke & J. Wiener and found applications in certain biomedical problems.     

Khasminskii-type theorems for stochastic functional differential equations with infinite delay

The classical Khasminskii-type theorem gives a powerful tool to examine the global existence of solutions for stochastic differential equations without the linear growth condition by the use of the Lyapunov functions. However, there is no such result for stochastic functional equations with infinite delay. The main aim of this paper is to establish the existence-and-uniqueness theorems of global solutions for stochastic functional differential equations with infinite delay.     

On the hyperbolicity of rapidly oscillating periodic solutions of functional differential equations

We consider periodic solutions of nonlinear functional differential equations with rational periods less than 2. We study the spectral properties of monodromy operators and state a hyperbolicity criterion for such solutions.__________Translated from Funktsionalnyi Analiz i Ego Prilozheniya, Vol. 39, No. 1, pp. 82–85, 2005Original Russian Text Copyright © by A. L. Skubachevskii and H.-O. WaltherThe first authors research was supported by the Mercator-Programm of the Deutsche Forschungsgemeinschaft, RFBR grant No. 04-01-00256, and Russian Ministry of Education and Science grant No. E02-1.0-131.Translated by A. L. Skubachevskii and H.-O. Walther     

Stability of solutions to delay differential equations with periodic coefficients of linear terms

Under study are the systems of quasilinear delay differential equations with periodic coefficients of linear terms. We establish sufficient conditions for the asymptotic stability of the zero solution, obtain estimates for solutions which characterize the decay rate at infinity, and find the attractor of the zero solution. Similar results are obtained for systems with parameters.     

Two periodic solutions of second-order neutral functional differential equations

In this paper, we consider a type of second-order neutral functional differential equations. We obtain some existence results of multiplicity and nonexistence of positive periodic solutions. Our approach is based on a fixed point theorem in cones.     

Linear measure functional differential equations with infinite delay

We use the theory of generalized linear ordinary differential equations in Banach spaces to study linear measure functional differential equations with infinite delay. We obtain new results concerning the existence, uniqueness, and continuous dependence of solutions. Even for equations with a finite delay, our results are stronger than the existing ones. Finally, we present an application to functional differential equations with impulses.     

Stability for impulsive functional differential equations with infinite delays

In this paper, some theorems of uniform stability and uniform asymptotic stability for impulsive functional differential equations with infinite delay are proved by using Lyapunov functionals and Razumikhin techniques. An example is also proved at the end to illustrate the application of the obtained results.