Existence of Periodic Solutions for Second-Order Ordinary <i>p</i>-Laplacian Systems

Abstract

In this paper, we study the variational principle and the existence of periodic solutions for a new class of second-order ordinary p-Laplacian systems. The variational principle is given by making use of two methods. We obtain three existence theorems of periodic solutions to this problem on various sufficient conditions on the potential function F(t,x) or nonlinearity ∇F(t,x). Four examples are presented to illustrate the feasibility and effectiveness of our results.

Keywords

• ordinary <i>p</i>-Laplacian system
• the variational principle
• periodic solutions
• the least action principle
• saddle point theorem