Infinitely many homoclinic solutions for a class of nonlinear difference equations. (English) Zbl 1340.39003
Summary: By using the symmetric mountain pass theorem, we establish some existence criteria to guarantee a class of nonlinear difference equation has infinitely many homoclinic orbits. Our conditions on the nonlinear term are rather relaxed and we generalize some existing results in the literature.
MSC:
39A12 | Discrete version of topics in analysis |
39A10 | Additive difference equations |
37C29 | Homoclinic and heteroclinic orbits for dynamical systems |