Homoclinic solutions of discrete prescribed mean curvature equations with mixed nonlinearities

Abstract

By using critical point theory, we obtain some new sufficient conditions for the existence of homoclinic solutions of discrete prescribed mean curvature equations with mixed nonlinearities for the unbounded potentials. To the best of our knowledge, there are no results on the existence of infinitely many homoclinic solutions to difference equations with mixed nonlinearities in the existing literature.