Existence and multiplicity of difference φ-Laplacian boundary value problems

Abstract

Concerned are the difference φ-Laplacian boundary value problems. The multiplicity result based on the lower and upper solutions method associated with Brouwer degree is applied to a difference φ-Laplacian eigenvalue problem. An existence result of at least three positive solutions is established for the eigenvalue problem with the parameter belonging to an explicit open interval. In addition, an example is given to illustrate the three solutions result. © 2013 Bai and Xu; licensee Springer.