Homoclinic solutions of 2nth-order difference equations containing both advance and retardation

Abstract

By using the critical point method, some new criteria are obtained for the existence and multiplicity of homoclinic solutions to a 2nth-order nonlinear difference equation. The proof is based on the Mountain Pass Lemma in combination with periodic approximations. Our results extend and improve some known ones.

Keywords

• homoclinic solutions
• 2nth-order
• nonlinear difference equations
• discrete variational theory
• 34c37
• 37j45
• 39a12