On the module containment of the almost periodic solution for a class of differential equations with piecewise constant delays

In the first part of this paper, we obtain a new property on the module containment for almost periodic functions. Based on it, we establish the module containment of an almost periodic solution for a class of differential equations with piecewise constant delays. In the second part, we investigate the existence, uniqueness and exponential stability of a positive almost periodic and quasi-periodic solution for a certain class of logistic differential equations with a piecewise constant delay. The module containment for the almost periodic solution is established.     

ON ALMOST PERIODIC SOLUTIONS OF AHIGHER ORDER ALMOST PERIODIC SYSTEM

1IntroductionConsiderthel'Ollowingdifferentialequationdx~~A(.t)x g(t,x),(l)dt.wherexeR",t6R,A(t)=(a,,(t)),,..istillnxncontinlloust'llllctiollmatrixinR,g(t,x)isanat-dimensionalcolltinuousfunctionvectorinRxR".Thepaper[l,21dealedwil;htheproblemontheexistence…     

Dynamics of Solutions and Approximation for Partial Functional Differential Equations with Delay

This work aims to investigate the existence and uniqueness of almost periodic solution for partial functional differential equations with delay. Here, we assume that the undelayed part is not necessarily densely defined and satisfies the well-known Hille–Yosida condition, the delayed parts are assumed to be almost periodic with respect to the first argument and Lipschitz continuous with respect to the second argument. Using the exponential dichotomy and the contraction mapping principle, some sufficient conditions are obtained for the existence and uniqueness of almost periodic solution.     

Uniqueness of weak solutions to a Keller-Segel-Navier-Stokes model with a logistic source

Applications of Mathematics - We prove a uniqueness result of weak solutions to the nD (n ? 3) Cauchy problem of a Keller-Segel-Navier-Stokes system with a logistic term.     

一个概周期锁相环路方程的概周期解的存在唯一性和渐近稳定性

本文研究了一个概周期锁相环路方程的概周期解的存在唯一性及渐近稳定性,得到了保证系统存在唯一渐近稳定的概周期解的充分条件     

无限时滞泛函微分方程概周期解的存在唯一性

对于无限时滞泛函微分方程,利用Liapunov泛函的方法,研究了方程概周期解的存在性、唯一性问题,得到了便于应用的概周期解的存在性、唯一性判据.     

Pseudo almost automorphic solutions for dissipative differential equations in Banach spaces

This work aims to study the existence and uniqueness of pseudo compact almost automorphic solution for some dissipative ordinary and functional differential equations. We prove the existence and uniqueness of pseudo compact almost automorphic solution for dissipative differential equations in Banach spaces and then we apply this result to show the existence of pseudo compact almost automorphic solutions for some functional differential equations.     

具有时滞的非线性微分方程的概周期解的存在性及唯一性

本文研究了一类具有时滞的非线性微分方程的有界解及概周期解的存在性及唯一性问题。利用变量替换和不动点方法及逼近法,我们得到了此类方程有界解和概周期解的存在性及唯一性的一些有趣的新结果。我们的结果大大改进和推广了文［２］的主要结果。     

Linear evolution equations in scales of Banach spaces

This work is devoted to the study of a class of linear time-inhomogeneous evolution equations in a scale of Banach spaces. Existence, uniqueness and stability for classical solutions is provided. We study also the associated dual Cauchy problem for which we prove uniqueness in the dual scale of Banach spaces. The results are applied to an infinite system of ordinary differential equations but also to the Fokker-Planck equation associated with the spatial logistic model in the continuum.     

带梯度算子二阶方程的渐近概周期解

利用渐近概周期函数的性质得到带梯度算子二阶方程的渐近概周期解在C（R^-）中的存在性．同时利用迭代法和线性常微分方程的概周期解的存在性和唯一性,得到R上此方程渐近概周期解的存在和唯一性．     

Almost automorphic solutions to some classes of partial evolution equations

We give in this work some sufficient conditions for the existence and uniqueness of almost automorphic (mild) solutions to some classes of partial evolution equations. Then we use our abstract results to discuss the existence and uniqueness of almost automorphic solutions to some partial differential equations.     

THE EXISTENCE, UNIQUENESS AND STABILITY OF ALMOST PERIODIC SOLUTION FOR A CLASS OF NONLINEAR SYSTEM

In this paper, we study the problems on the existence, uniqueness and stability of almost periodic solution for a class of nonlinear system. Using fixed point theorem and Lyapunov functional, the sufficient conditions are given which guarantee the existence, uniqueness and stability of almost periodic solution for the system.     

时滞Lotka-Volterra竞争型系统的概周期解

研究具有离散时滞的N-种群Lotka-Volterra竞争型系统，得到了系统存在唯一性概周期解的一组充分条件。     

一类非自治随机微分方程的均方渐近概周期解

本文研究了一类在可分Hilbert空间中的非自治随机微分方程的均方渐近概周期解.利用"Acquistapace-Terreni"条件,开方族和Banach不动点原理讨论了该类随机微分方程的均方渐近概周期解的存在唯一性,推广了该类随机微分方程的均方概周期解的存在唯一性问题.     

EXISTENCE AND GLOBAL ATTRACTIVITY OF ALMOST PERIODIC SOLUTION TO A DELAYED DIFFERENTIAL EQUATION

A new fixed point theorem is presented and sufficient conditions are obtained for the existence, uniqueness and global attractivity of a positive almost periodic solution to a delayed differential equation with almost periodic factors.     

THE EXISTENCE AND UNIQUENESS AND STABILITY OF ALMOST PERIODIC SOLUTIONS FOR FUNCTIONAL DIFFERENTIAL EQUATIONS WITH INFINITE DELAYS

ＴＨＥＥＸＩＳＴＥＮＣＥＡＮＤＵＮＩＱＵＥＮＥＳＳＡＮＤＳＴＡＢＩＬＩＴＹＯＦＡＬＭＯＳＴＰＥＲＩＯＤＩＣＳＯＬＵＴＩＯＮＳＦＯＲＦＵＮＣＴＩＯＮＡＬＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＳＷＩＴＨＩＮＦＩＮＩＴＥＤＥＬＡＹＳＷＡＮＧＱＵＡＮＨＮＹ...     

概周期系统概周期解的存在唯一性

应用构造Ляпунов函数的方法，讨论了非线性微分方程系概周期解的存在唯一性.同时给出了Liénard方程存在唯一概周期解的一组充分条件.     

Existence and uniqueness of pseudo almost periodic solutions to some abstract partial neutral functional-differential equations and applications

The paper considers the existence and uniqueness of pseudo almost periodic (mild) solutions to some classes of first-order partial neutral functional-differential equations. Upon making some suitable assumptions, existence and uniqueness results are obtained. Applications include both a partial integro-differential equation arising in control systems and the scalar reaction-diffusion equation with delay.     

Existence and asymptotic behavior of solutions of semilinear Cauchy problems with non dense domain via extrapolation spaces

In this work we study the existence and the uniqueness of bounded and almost periodic, asymptotic almost periodic or Eberlein-weak periodic solutions to the Cauchy problems with non dense domain.     

ON EXISTENCE， UNIQUENESS AND REGULARITY OF STEADY STATE SOLUTIONS TO THE BASIC SEMICONDUCTOR EQUATIONS

ＯＮＥＸＩＳＴＥＮＣＥ，ＵＮＩＱＵＥＮＥＳＳＡＮＤＲＥＧＵＬＡＲＩＴＹＯＦＳＴＥＡＤＹＳＴＡＴＥＳＯＬＵＴＩＯＮＳＴＯＴＨＥＢＡＳＩＣＳＥＭＩＣＯＮＤＵＣＴＯＲＥＱＵＡＴＩＯＮＳＷａｎｇＹｕａｎｍｉｎｇ（王元明）ＦａｎＪｉｓｈａｎ（樊继山）（Ｄｅｐｔ...