The Existence of Multiple Periodic Solutions of Nonautonomous Delay Differential Equations

Huafeng Xiao,Bo Zheng

doi:10.1155/2011/829107

Abstract

We study the multiplicity of periodic solutions of nonautonomous delay differential equations which are asymptotically linear both at zero and at infinity. By making use of a theorem of Benci, some sufficient conditions are obtained to guarantee the existence of multiple periodic solutions.

Highlights

The existence and multiplicity of periodic solutions of delay differential equations have received a great deal of attention
In 1962, Jones 1 firstly investigated the existence of periodic solutions to the following scalar equation: u t −au t − 1 1 u t
Various fixed point theorems have been used to study the existence of periodic solutions of delay differential equations cf. 2

Summary

Introduction

The existence and multiplicity of periodic solutions of delay differential equations have received a great deal of attention. Various fixed point theorems have been used to study the existence of periodic solutions of delay differential equations cf 2 . They reduced the existence of periodic solutions of 1.2 to that of critical points of an associated variational functional.

Objectives

Results

Conclusion