Periodic solutions of abstract neutral functional differential equations with infinite delay

We establish the existence of mild solutions and periodic mild solutions for a class of abstract first-order non-autonomous neutral functional differential equations with infinite delay in a Banach space. This research was supported by FONDECYT-CONICYT, Grant 1050314.     

Global solutions for abstract neutral differential equations

We study the existence of global solutions for a class of abstract neutral differential equation defined on the whole real axis. Some concrete applications related to ordinary and partial differential equations are considered.     

Periodic solutions of neutral fractional differential equations

We characterize the existence of periodic solutions for some abstract neutral functional fractional differential equations with finite delay when the underlying space is a UMD space.     

Global solutions for abstract impulsive neutral differential equations

We study the existence of mild solutions for a class of impulsive neutral functional differential equation defined on the whole real axis. Some concrete applications to ordinary and partial neutral differential equations with impulses are considered.     

Periodic solutions of neutral nonlinear system of differential equations with functional delay

We study the existence of periodic solutions of the nonlinear neutral system of differential equations of the form

     

Periodic solutions for a kind of second order neutral functional differential equations

In this paper, criteria are established for the existence of periodic solutions to a second order sublinear neutral differential equation. Our method is based on careful a priori estimation and continuation theorem, and our sublinear condition is an improvement of the boundedness condition in some recent results.     

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.     

On a class of abstract neutral functional differential equations

By using the theory of semigroups of growth α, we discuss the existence of mild solutions for a class of abstract neutral functional differential equations. A concrete application to partial neutral functional differential equations is considered.     

Periodic solutions of retarded functional differential equations

The classical criterion for the existence of a periodic solution of a forced, linear, retarded functional differential equation (rfde) references the solution of an adjoint equation which is an advanced functional differential equation. This paper introduces a new criterion which does away with the (anti-causal) advanced functional differential equation.     

Almost automorphic solutions for abstract functional differential equations

For abstract linear functional differential equations with an almost automorphic forcing term, we establish a result on the existence of almost automorphic solutions, which extends the classical theorem due to Massera on the existence of periodic solutions for linear periodic ordinary differential equations.     

高阶非线性中立型微分方程的周期解

利用k-集压缩延拓理论 ,研究了一类高阶非线性中立型微分方程周期解的存在性 ,推广了文 [1 ],[2 ]的相应结果 .     

Asymptotic behavior of solutions to abstract functional differential equations

In this paper, a new approach is provided to study the asymptotic behavior of functions. A Tauberian theorem is improved and applied to describe the asymptotic behavior of abstract functional differential equations of the form

     

Almost periodic solutions of neutral functional differential equations

We study a nonlinear neutral functional differential equation. Applying the properties of almost periodic function and exponential dichotomy of linear system as well as Krasnoselskii’s fixed point theorem, we establish the conditions for the existence of almost periodic solution of the equations.