Boundedness of solutions for a class of second-order periodic systems

Abstract

In this paper we study the following second-order periodic system: x'' + V ' (x) + p (x, t) = 0, where V (x) has a singularity. Under some assumptions on the V (x) and p (x, t) by Ortega' small twist theorem, we obtain the existence of quasi-periodic solutions and boundedness of all the solutions. © 2013 Shunjun Jiang and Yan Ding.