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.     

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.     

半线性微分方程的概自守与伪概自守解

在Banach空间中,利用发展系统的算子半群理论和Banach压缩原理,在半线性微分方程x′（t）=A（t）x（t）＋f（t,x（t））满足一定的条件下,证明了其概自守与伪概自守mild解的存在性与唯一性．     

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.     

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d/dt(x(t))-∫0∞Q(s)x(t+s)ds)=A(t,x(t))x(t)+f(t,xt)的周期解问题.利用矩阵测度和Kranoselski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.     

具有无穷时滞中立型泛函微分方程概周期解的存在性

对具有无穷时滞中立型泛函微分方程，本文利用Ｌｉａｐｕｎｏｖ泛函，建立概周期解的存在性定理．     

一类中立型泛函微分方程伪概周期解的存在性

通过引入算子F,结合伪概周期函数理论及一些分析技巧,讨论了一类带逐段常变量的二阶中立型泛函微分方程伪概周期解的存在性.     

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.     

具无限时滞的中立型随机泛函微分方程解的存在唯一性

The main aim of this paper is to establish the existence-and-uniqueness theorem for neutral stochastic functional differential equations with infinite delay at phase space BC（（-∞, 0]; R^n） An example is given for illustration.     

一类具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$ \frac{\rm d}{{\rm d}t}\left(x(t)-\int_{-\infty}^{0}g(s,x(t+s)){\rm d}s\right) =A(t,x(t))x(t)+f(t,x_t)$的周期解问题,利用重合度理论中的延拓定理得到了周期解的存在性和唯一性条件;特别地,当$g(s,x)\equiv 0, A(t,x)=A(t)$时, 给出了存在唯一稳定周期解的条件.     

Existence of $\mu$-pseudo almost automorphic solutions to abstract partial neutral functional differential equations with infinite delay

In this article, we introduce and investigate the concept of $\mu$-Stepanov-like pseudo almost automorphic functions of class $h$ and class infinity via measure theory. We present new results on completeness and composition theorems for the space of such functions. To illustrate our main results, we provide some applications to an abstract partial neutral functional differential equation with infinite delay.     

Weighted pseudo almost automorphic functions and WPAA solutions to semilinear evolution equations

In this paper, we reveal several basic properties about nonlinear vector-valued weighted pseudo almost automorphic functions, including equivalence, completeness, translation invariance, composition theorem, and convolution theorem of these functions. We also give some concrete examples to illustrate our results. Finally, we obtain a new existence theorem of nonlinear weighted pseudo almost automorphic solutions for semilinear evolution equations in Banach spaces.     

Pseudo almost automorphic solutions for some partial functional differential equations with infinite delay

In this work, we study the existence of pseudo almost automorphic solution for some partial functional differential equations with infinite delay. We assume that the undelayed part is not necessarily densely defined and satisfies the Hille–Yosida condition. We use the variation of constant formula developed recently in 1 Hino, Y, Murakami, S and Naito, T. 1991. “Functional Differential Equations with Infinite Delay”. In Lecture Notes in Mathematics, Vol. 1473, New York: Springer-Verlag.  [Google Scholar] to get the existence and uniqueness of pseudo almost automorphic solution when the linear equation has an exponential dichotomy. We also give an application of the abstract results to a Lotka–Volterra model with diffusion.     

μ‐Pseudo almost automorphic solutions of abstract fractional integro‐differential neutral equations with an infinite delay

The aim of this work is to study μ‐pseudo almost automorphic solutions of abstract fractional integro‐differential neutral equations with an infinite delay. Thanks to some restricted hypothesis on the delayed data in the phase space, we ensure the existence of the ergodic component of the desired solution. Copyright © 2016 John Wiley & Sons, Ltd.     

STABILITY AND ALMOST PERIODIC SOLUTIONS OF NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATIONS WITH INFINITE DELAY

Itiswellknownthattheexistenceofalmostperiodicsolutionsiscloselyrelatedtothestabilityofsolutions.Forfunctionaldifferentialequationswithinfinitedelay,Y.Hin.[5'6]studiedtheproblemsontheexistenceofalmostperiodicsolutionsandthestability.However,therearefewpapersll2]dealingwithneutralfunctionaldifferentialequationswithinfinitedelay.Inthepresentpaper,forneutralfunctionaldifferentialequationswithinfinitedelay,weprovetheinherencetheoremfortheuniformlystableoperatorD(t),definethestabilitywithrespecttot…     

Composition of Stepanov-like pseudo almost automorphic functions and applications to nonautonomous evolution equations

In this paper, we establish a new composition theorem about Stepanov-like pseudo almost automorphic functions under the local Lipschitz condition. Using this composition theorem, we also study the existence and uniqueness of pseudo almost automorphic solutions for nonautonomous evolution equations. Our results extend many recent known ones on these topics.     

Weighted pseudo almost periodic solutions of N-th order neutral differential equations with piecewise constant arguments

In this work, we present some existence theorems of weighted pseudo almost periodic solutions for N-th order neutral differential equations with piecewise constant argument by means of weighted pseudo almost periodic solutions of relevant difference equations.     

Existence of pseudo almost automorphic mild solutions to stochastic fractional differential equations

Fractional stochastic differential equations have gained considerable importance due to their application in various fields of science and engineering. This paper is concerned with the square-mean pseudo almost automorphic solutions for a class of fractional stochastic differential equations in a Hilbert space. The main objective of this paper is to establish the existence and uniqueness of square-mean pseudo almost automorphic mild solutions to a linear and semilinear case of these equations. A new set of sufficient conditions is obtained to achieve the required result by using the stochastic analysis theory and fixed point strategy. Finally, an example is provided to illustrate the obtained theory.