Homoclinic solutions in periodic partial difference equations

Abstract

By using critical point theory in combination with periodic approximations, we obtain novel sufficient conditions for the existence of nontrivial homoclinic solutions for a class of periodic partial difference equations with sign-changing mixed nonlinearities. Notably, in certain specific cases, a necessary and sufficient condition is also established.

Keywords

• homoclinic solution
• partial difference equation
• discrete nonlinear schrödinger equation
• critical point theory
• periodic approximation
• primary: 39a14