Existence of periodic solutions for abstract neutral non-autonomous equations with infinite delay

Abstract

In this paper, by using Sadovskii fixed point theorem, we study the existence of solutions and periodic solutions for a class of abstract neutral functional evolution equations with infinite delay. An example is presented in the end to show the applications of the obtained results.

Global Periodic Attractors for a Class of Infinite Dimensional Dissipative Dynamical Systems

“…Proposition 1 (see [11]) The family of operators is continuous in t in the uniform operator topology uniformly for s.…”

“…U t s t s    0 Lemma 1 (see [11]) Consider the initial value problem (1.1) in E. If 1)-4) hold, then, for any , there exists a unique continuous function such that…”

“…In is a negative Laplacian operator, and A generates an analytic semigroup so that the theory of the fractional power has been used effectively there. However, their results clearly cannot apply to Equation (1.1) with A t is non-autonomous which is a more general and maybe more important case [11]. So we will use the appropriate assumptions to overcome the difficulty for the non-autonomous operator   A t .…”

Existence of a mild solution for an impulsive nonlocal non-autonomous neutral functional differential equation

“…For more details on non-autonomous differential equations, we refer to monograph [21,22], and papers [1][2][3][4][5][6][7][8]11,12,26,27,[29][30][31][32][33][34][35] and references cited therein.…”

Periodic solutions of abstract neutral functional differential equations with infinite delay

“…In most of these works the operator A is independent of the time t. Furthermore, recently an ANFDE of type (1.1), with A(t) dependent on t, has been studied by Fu and Liu [12]. The technique used in [12] requires that the range of g, in short R(g), is included in D(A).…”