Multiplicity results for periodic solutions to a class of second order delay differentialequations

Zhiming Guo; Xiaomin Zhang

doi:10.3934/cpaa.2010.9.1529

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2010, Volume 9, Issue 6: 1529-1542. Doi: 10.3934/cpaa.2010.9.1529

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Multiplicity results for periodic solutions to a class of second order delay differential equations

Zhiming Guo^1, and
Xiaomin Zhang^1,

1.
School of Mathematics and Information Sciences, Guangzhou University, Guangzhou, 510006

Received: November 2009

Revised: March 2010

Published: November 2010

Abstract / Introduction Related Papers Cited by

Abstract

In this paper, we study the following second order delay differential equation

$x''(t)=-f(x(t), x(t-\tau)).$

When $f$ possesses a symmetric property and grows asymptotically linear both at zero and at infinity, some new results for the existence and multiplicity of periodic solutions are obtained by using the critical point theory and $S^1$ geometrical index theory.

Keywords:

Second order delay differential equations,
multiple periodic solutions,
Hamiltonian systems,
critical point theory,
$S^1$ geometrical index theory.

Mathematics Subject Classification: Primary: 34K13, 34K18; Secondary: 58E50.

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