On homoclinic solutions for a second order difference equation with <i>p</i>-Laplacian

Abstract

In this paper, we obtain conditions under which the difference equation \begin{document}$-Δ ≤ft( a(k)φ _{p}(Δ u(k-1))) +b(k)φ_{p}(u(k))=λ f(k, u(k)), \;\;k∈\mathbb{Z}, $ \end{document} has infinitely many homoclinic solutions. A variant of the fountain theorem is utilized in the proof of our theorem. Some known results in the literature are extended and complemented.