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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 906972, 10 pages
http://dx.doi.org/10.1155/2013/906972
Research Article

Lazer-Leach Type Conditions on Periodic Solutions of Liénard Equation with a Deviating Argument at Resonance

School of Mathematical Sciences, Capital Normal University, Beijing 100048, China

Received 28 February 2013; Accepted 15 April 2013

Academic Editor: Wing-Sum Cheung

Copyright © 2013 Zaihong Wang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We study the existence of periodic solutions of Liénard equation with a deviating argument where are continuous and is -periodic, is a constant, and is a positive integer. Assume that the limits and exist and are finite, where . We prove that the given equation has at least one -periodic solution provided that one of the following conditions holds: , for all , for all , for all , for all