Multiple solutions for nonsmooth fractional Hamiltonian systems

This paper investigates the existence of infinitely many pairs of nontrivial solutions for a class of nonsmooth fractional Hamiltonian systems, where the energy functional associated with the system is not continuously differentiable and does not satisfy the Palais-Smale condition. By considering a potential function of the form \(V(t,x)=-K(t,x)+W(t,x)\), where K and W are continuously differentiable functions with specific growth conditions, we extend existing results to cover cases involving nonsmoothness and certain types of nonlocal interactions. The study is based on variational methods and critical point theory, and we establish several theorems that guarantee the existence of multiple solutions under appropriate hypotheses on the nonlinearities of the system. These results contribute to the understanding of nonsmooth fractional Hamiltonian systems, particularly when traditional compactness conditions fail.