Periodic solutions for nonlocal $p(t)$-Laplacian systems

Abstract

The purpose of this paper is to investigate the existence of periodic solutions for a class of nonlocal p(t)-Laplacian systems. When the nonlinear term is p +-superlinear at infinity, some new solvability conditions of nontrivial periodic solutions are obtained by using a version of the local linking theorem. A major point is that we ensure compactness without the well-known Ambrosetti-Rabinowitz type superlinearity condition. In addition, by applying the saddle point theorem, we established the existence of at least one periodic solution for such problems with a p-subquadratic potential.