The Nehari manifold method for discrete fractional p-Laplacian equations

Abstract

Abstract The aim of this paper is to investigate the multiplicity of homoclinic solutions for a discrete fractional difference equation. First, we give a variational framework to a discrete fractional p-Laplacian equation. Then two nontrivial and nonnegative homoclinic solutions are obtained by using the Nehari manifold method.

Keywords

• Discrete fractional p-Laplacian
• Homoclinic solutions
• Nehari manifold