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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 937128, 7 pages
http://dx.doi.org/10.1155/2013/937128
Research Article

Nonperiodic Damped Vibration Systems with Asymptotically Quadratic Terms at Infinity: Infinitely Many Homoclinic Orbits

School of Mathematics and Statistics, Anyang Normal University, Anyang, Henan 455000, China

Received 10 September 2013; Accepted 10 October 2013

Academic Editor: Dumitru Motreanu

Copyright © 2013 Guanwei Chen. 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 a class of nonperiodic damped vibration systems with asymptotically quadratic terms at infinity. We obtain infinitely many nontrivial homoclinic orbits by a variant fountain theorem developed recently by Zou. To the best of our knowledge, there is no result published concerning the existence (or multiplicity) of nontrivial homoclinic orbits for this class of non-periodic damped vibration systems with asymptotically quadratic terms at infinity.