EXISTENCE OF POSITIVE PERIODIC SOLUTIONS FOR INFINITE DELAY FUNCTIONAL DIFFERENTIAL EQUATIONS

In this paper, the existence of positive periodic solutions for infinite delay functional differential equations(FDEs for short) is discussed by utilizing a fixed point theorem on a cone in Banach space. Some results on the existence of positive periodic solutions are derived.     

EXISTENCE OF MILD SOLUTIONS TO NEUTRAL FRACTIONAL DIFFERENTIAL EQUATIONS WITH INFINITE DELAY

In this paper, we consider the existence of mild solution to a class of neutral fractional differential equations with infinite delay. By means of fixed points methods, we obtain some sufficient conditions for the existence and uniqueness of mild solutions, which extend some known results.     

预解算子控制的无穷时滞分数阶微分方程解的存在性

本文研究了一类预解算子控制的具有无穷时滞的分数阶泛函微分方程.利用解析预解算子理论和不动点定理,得到了具有无穷时滞分数阶微分方程适度解的存在性,推广和改进了一些已知的结果.     

PERIODIC SOLUTIONS TO NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATIONS WITH INFINITE DELAY

A new and convenient method is used to study the existence of periodic solutions to neutral functional differential equations with infinite delay. A new criterion for the existence of periodic solutions is obtained in this paper.     

CONTROLLABILITY OF ABSTRACT RETARDED FUNCTIONAL DIFFERENTIAL SYSTEMS WITH INFINITE DELAY

This paper is concerned with the controllability of retarded functional differential systems with infinite delay in a general Banach space, via a fixed point approach. Sufficient conditions for controllability are established by using the Leray-Schauder alternative. An example is given to illustrate the results.     

STABILITY OF NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATIONS WITH INFINITE DELAY

In the phase space (Ch, |·|h), by using the Liapunov functional approach, sufficient and necessary criteria for the uniform stability and uniformly asymptotic stability of solutions to neutral-functional differential equations with infinite delay are established. We also prove that the uniformly asymptotic stability of the solutions implies the existence of the bounded ones.     

THE RAZUMIKHIN TYPE THEOREMS OF STABILITY AND BOUNDEDNESS FOR FUNCTIONAL DIFFERENTIAL EQUATIONS WITH INFINITE DELAY

LetR"bethen-dimensionalrealspace,andBCbethesetofallboundedandcolltinuousfunctionsdefinedon(--co,0]withvaluesinRe.FOranypinBC,letlaal=supIg(0)I.Then(BC,I'l)isaBanachspace.F'Orally6相似文献   

STABILITY OF THE SOLUTIONS TO STOCHASTIC FUNCTIONAL DIFFERENTIAL EQUATIONS WITH INFINITE DELAY

In this paper,we obtain the stability of solutions to stochastic functional differential equations with infinite delay at phase space BC((-∞,0];Rd),under non-Lipschitz condition with Lipschitz condition being considered as a special case and a weakened linear growth condition by means of the corollary of Bihari inequality.     

无穷时滞泛函微分方程的正周期解

利用范数形式的锥拉伸和锥压缩不动点定理讨论具有无穷时滞泛函微分方程的周期解问题,获得了正周期解的存在性定理,并给出了定理的若干应用.     

时滞微分方程和脉冲时滞微分方程解的存在唯一性

本文研究了时滞微分方程的问题.利用上下解作为耦合初始迭代得到一个收敛于此方程解的单调序列的方法,获得了时滞方程和脉冲时滞微分方程解的存在唯一性结果,推广了文献[3,5]的相关结果.     

无穷时滞泛函微分方程周期解的存在性

本文利用Mawhin度的方法在较容易判别和较简单的假设下,得到ω周期方程存在周期解．     

BOUNDARY VALUE PROBLEMS WITH INTEGRO CONDITION FOR RETARDED FUNCTIONAL DIFFERENTIAL EQUATIONS

1 IntroductionIn recent years) there were many results of studying boundary value problemsfor functional differential equations [1-5]. But the boundary conditions are allDirichlet's type. In this paper, we will study a kind of boundary value problemswitb integro boundary condition fOr the functional differential equdtionswhere f(t, yt, x, y) is a continuous real function defined on the set fl = [0, T] xC. x R', and is continuously differentiable with respect to each variable x, y;p E C. = C…     

具有无穷时滞泛函微分方程的周期解

讨论具有无穷时滞中立型泛函微分方程的周期解问题.利用矩阵测度和Krasnoselskii不动点定理得到了周期解的存在性和唯一性定理;特别地,当Q（s）为零矩阵,A（t,x）=A（t）时给出了存在唯一稳定的周期解的条件.     

CONTROLLABILITY OF NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATIONS WITH INFINITE DELAY

In this article, we give sufficient conditions for controllability of some partial neutral functional differential equations with infinite delay. We suppose that the linear part is not necessarily densely defined but satisfies the resolvent estimates of the Hille-Yosida theorem. The results are obtained using the integrated semigroups theory. An application is given to illustrate our abstract result.     

无限滞后测度泛函微分方程的平均化

本文研究了无限滞后测度泛函微分方程的平均化.利用广义常微分方程的平均化方法,在无限滞后测度泛函微分方程可以转化为广义常微分方程的基础上,获得了这类方程的周期和非周期平均化定理,推广了一些相关的结果.     

一类重特征方程柯西问题的存在唯一性

讨论了一类高维重特征方程栖西问题存在唯一性中的离散现象，证明发池方程的参数取某些值时存在唯一性有离散现象发生。并建立了存在唯一性与黎曼问题的联系。     

INERTIAL MANIFOLDS FOR NONAUTONOMOUS SEMILINEAR PARABOLIC PARTIAL DIFFERENTIAL EQUATIONS WITH TIME DELAYS

The present paper deals with the long-time behavior of a class of nonautonomous retarded semilinear parabolic differential equations. When the time delays are small enough and the spectral gap conditions hold, the inertial manifolds of the nonautonomous retard parabolic equations are constructed by using the Lyapunov-Perron method.     

EXISTENCE RESULTS FOR IMPULSIVE NEUTRAL EVOLUTION DIFFERENTIAL EQUATIONS WITH STATE-DEPENDENT DELAY

This paper is mainly concerned with the existence of mild solutions to a first order impulsive neutral evolution differential equations with state-dependent delay. By suitable fixed point theorems combined with theories of evolution systems,we prove some existence theorems. As an application,an example is also given to illustrate the obtained results.     

EXISTENCE OF MILD SOLUTIONS TO SEMILINEAR FRACTIONAL ORDER FUNCTIONAL DIFFERENTIAL EQUATIONS

In this paper,we use the analytic semigroup theory of linear operators and fixed point method to prove the existence of mild solutions to a semilinear fractional order functional differential equations in a Banach space.     

BOUNDARY VALUE PROBLEMS FOR nTH ORDER RETARDED FUNCTIONAL DIFFERENTIAL EQUATIONS

1IntroductionTherearemanyresultsofstudyingboundaryvalueproblemsforsecondorderfunctionaldifferentialequations['I'].Butthestudyofboundaryvalueproblemsforhigherorderfunctionaldifferentialequationsrarelyappears.Inthispaper,wediscussthefollowingntypesofboundaryvalueproblemsforniborderfunctionaldifferentialequationswheref(t,yi,xo3xl)'',x.--1)isacontinuousrealfunctiondefinedonthesetA=[0,T]xCdxR.Forafixedr>0,letCrgC([--r,0],R)bethespaceofcontinuousfunctionon[--r,0]withthenormdefinedbyIIWll=supl…