Periodic Solutions for Some Nondensely Nonautonomous Partial Functional Differential Equations in Fading Memory Spaces

被引：6

作者：

Kpoumiè M.E.-K. ^{[1
,2
]}

Ezzinbi K. ^{[3
]}

Békollè D. ^{[1
]}

机构：

[1] Departement de Mathematiques, Faculté des Sciences, Université de Yaoundé I, B.P. 812, Yaoundé

[2] Département de Mathématiques et Informatique, École de Géologie et d’Exploitation Minière, Université de Ngaoundéré, Ngaoundéré

[3] Département de Mathématiques, Faculté des Sciences Semlalia, Université Cadi Ayyad, B.P. 2390, Marrakesh

来源：

Differential Equations and Dynamical Systems | 2018年 / 26卷 / 1-3期

关键词：

Evolution family; Fading memory spaces; Nonautonomous equations; Periodic solutions; Stability conditions; Variation of constants formula;

D O I：

10.1007/s12591-016-0331-9

中图分类号：

学科分类号：

摘要：

The aim of this work is to study the existence of a periodic solution for some nondensely nonautonomous partial functional differential equations with infinite delay in Banach spaces. We assume that the linear part is not necessarily densely defined and generates an evolution family. We use Massera’s approach (Duke Math 17:457–475, 1950), we prove that the existence of a bounded solution on R+ implies the existence of an ω-periodic solution. In nonlinear case, we use a fixed point for multivalued maps to show the existence of a periodic solution. Finally, we consider a reaction diffusion equation with delay to illustrate the main results of this work. © 2016, Foundation for Scientific Research and Technological Innovation.

引用

页码：177 / 197

页数：20

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