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

Abstract

Abstract The purpose of this paper is to investigate the existence of periodic solutions for a class of nonlocal p(t) $p(t)$-Laplacian systems. When the nonlinear term is p+ $p^{+}$-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− $p^{-}$-subquadratic potential.

Keywords

• Variational methods
• p ( t ) $p(t)$ -Laplacian systems
• Nonlocal problems
• Critical point
• Periodic solution