Existence of homoclinic orbits for a class of nonlinear functional difference equations

Abstract

By using critical point theory, we prove the existence of a nontrivial homoclinic orbit for a class of nonlinear functional difference equations. Our conditions on the nonlinear term do not need to satisfy the well-known global Ambrosetti-Rabinowitz superquadratic condition.

Keywords

• Homoclinic orbit
• difference equation
• critical point theory