Existence of infinitely many homoclinic solutions for a class of $p-$Laplacian Hamiltonian systems

Abstract

 In this paper, we introduce a general and weak sufficient condition that guarantees the existence of infinitely many homoclinic solutions for a class of $p-$Laplacian Hamiltonian systems. Our findings are established using a new symmetric mountain pass theorem developed by Kajikia. We extend and refine several recent results from the literature and provide examples to demonstrate our key theoretical contributions.