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November  2010, 9(6): 1529-1542. doi: 10.3934/cpaa.2010.9.1529

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

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

Received  November 2009 Revised  March 2010 Published  August 2010

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.

Citation: Zhiming Guo, Xiaomin Zhang. Multiplicity results for periodic solutions to a class of second order delay differential equations. Communications on Pure & Applied Analysis, 2010, 9 (6) : 1529-1542. doi: 10.3934/cpaa.2010.9.1529
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