Standing Waves Solutions for the Discrete Schrödinger Equations with Resonance

Abstract

In this paper, by using linking methods, we obtain the existence of the nontrivial standing wave solutions for the discrete nonlinear Schrödinger equations with resonance and unbounded potentials. In order to prove the existence of standing wave solutions, we give resonant condition to find a bounded critical sequence, and we show that such a sequence guarantees the existence of one nontrivial standing wave solution in $$l^{2}$$ l 2 when the nonlinearity is resonant and the potential is unbounded. To the best of the our knowledge, there is no existence results for the discrete nonlinear Schrödinger equations with resonance in the literature.