Emden-Fowler problem for discrete operators with variable exponent

Abstract

In this article, we prove the existence of homoclinic solutions for a p(.)-Laplacian difference equation on the set of integers, involving a coercive weight function and a reaction term satisfying the Ambrosetti-Rabinowitz condition. The proof of the main result is obtained by using critical point theory combined with adequate variational techniques, which are mainly based on the mountain pass theorem.

Keywords

• Difference equations
• discrete p(.)-Laplacian
• homoclinic solution, mountain pass lemma