Boundedness of Solutions for a Class of Second-Order Periodic Systems

Abstract

In this paper we study the following second-order periodic system: $x^{\prime \prime }+V^{\prime }(x)+p(x,t)=\mathrm{0,}$ 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.