Infinitely many homoclinic solutions for nonlinear p -Laplacian partial difference equations without Ambrosetti-Rabinowitz condition

Abstract

In this paper, we explore the existence of infinitely many homoclinic solutions for nonlinear p -Laplacian partial difference equations by variational methods in combination with the Symmetric Mountain Pass Theorem. Our obtained results extend and refine existing results by relaxing the Ambrosetti-Rabinowitz condition and generalizing the constraints on nonlinear terms. Additionally, three illustrative examples are presented to demonstrate the practical applications of our theorems.