Global continuum and multiple positive solutions to one-dimensional p-Laplacian boundary value problem

Abstract

Abstract We show the global structure of the set of positive solutions of a discrete Dirichlet problem involving the p-Laplacian difference operator suggesting suitable conditions on the weight function and nonlinearity. We obtain existence and multiplicity of positive solutions for λ lying in various intervals in R $\mathbb {R}$ by using the directions of a bifurcation and the Picone-type identity for discrete p-Laplacian operators.

Keywords

• Difference equation
• p-Laplacian
• Positive solutions
• Bifurcation
• Picone-type identity