Existence of two homoclinic solutions for a nonperiodic difference equation with a perturbation

Abstract

In the present paper, with the combination of a compactness lemma and variational techniques, we establish a sufficient condition to guarantee the existence of two nontrivial homoclinic solutions for a nonperiodic fourth-order difference equation with a perturbation. Our result generalizes and improves some known results.

Keywords

• nonperiodic fourth-order difference equation
• homoclinic solution
• mountain pass theorem
• variational technique