Open Access Research

The Clark dual and multiple periodic solutions of delay differential equations

Huafeng Xiao*, Jianshe Yu and Zhiming Guo

Author Affiliations

College of Mathematics and Information Sciences, Guangzhou University, Guangzhou, 510006, PRC

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Boundary Value Problems 2011, 2011:44 doi:10.1186/1687-2770-2011-44

Published: 11 November 2011

Abstract

We study the multiplicity of periodic solutions of a class of non-autonomous delay differential equations. By making full use of the Clark dual, the dual variational functional is considered. Some sufficient conditions are obtained to guarantee the existence of multiple periodic solutions.

2000 Mathematics Subject Classification: 34K13; 34K18.

Keywords:
periodic solution; Clark dual; Morse-Ekeland index; delay differential equation; asymptotic linearity