In this paper, we give a general and weak sufficient condition to guaranteeing the existence and infinite homoclinic solutions for some classes of differential equations, in particular for a class of Hamiltonian systems. We illustrate our main theoretical results by an application.

This paper concerns the ground state solutions for the partial differential equations known as the Dirac equations. Under suitable assumptions on the nonlinearity, we show the existence of nontrivial and ground state solutions.