Existence and multiplicity of homoclinic solutions for second‐order nonlinear difference equations with Jacobi operators

Abstract

In this paper, a nonperiodic discrete nonlinear equation with Jacobi operators is considered. By using the critical point theory, we establish some new sufficient conditions on the existence and multiplicity of homoclinic solutions. Recent results are generalized and significantly improved. Furthermore, our results greatly improve some existing ones even for some special cases. Copyright © 2016 John Wiley & Sons, Ltd.