Perturbed Schrödinger lattice systems with superlinear terms: Multiplicity of homoclinic solutions

We study a class of perturbed Schrödinger lattice systems without even conditions. Based on variational methods, we obtain the existence of two nontrivial homoclinic solutions. In particular, one of them is a ground state homoclinic solution, i.e., nontrivial homoclinic solution with least possible energy of this equation, and it is also a local minimizer of the action functional. To the best of our knowledge, there is no published result focusing on the systems.