Journal of Applied Mathematics
Volume 2012 (2012), Article ID 615303, 13 pages
http://dx.doi.org/10.1155/2012/615303
Research Article

Existence and Uniqueness of Homoclinic Solution for a Class of Nonlinear Second-Order Differential Equations

Lijuan Chen and Shiping Lu

School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, China

Received 11 September 2012; Accepted 13 November 2012

Academic Editor: Julián López-Gómez

Copyright © 2012 Lijuan Chen and Shiping Lu. 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

The authors study the existence and uniqueness of a set with -periodic solutions for a class of second-order differential equations by using Mawhin's continuation theorem and some analysis methods, and then a unique homoclinic orbit is obtained as a limit point of the above set of -periodic solutions.