Abstract and Applied Analysis
Volume 2011 (2011), Article ID 106214, 28 pages
http://dx.doi.org/10.1155/2011/106214
Research Article

Lagrangian Stability of a Class of Second-Order Periodic Systems

Shunjun Jiang1 and Fang Fang2

1College of Sciences, Nanjing University of Technology, Nanjing 210009, China
2Department of Basic Course, Nanjing Institute of Technology, Nanjing 211167, China

Received 18 November 2010; Accepted 8 June 2011

Academic Editor: Jean Pierre Gossez

Copyright © 2011 Shunjun Jiang and Fang Fang. 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 following second-order periodic system: x′′+V′(x)+p(t)=0 where V(x) has a singularity and p(t)=p(t+1). Under some assumptions on the V(x) and p(t), by Moser's twist theorem we obtain the existence of quasiperiodic solutions and boundedness of all the solutions.