Existence and Nonexistence of Solutions to <i>p</i>-Laplacian Problems on Unbounded Domains

Abstract

In this article, using a fixed point index theorem on a cone, we prove the existence and multiplicity results of positive solutions to a one-dimensional p-Laplacian problem defined on infinite intervals. We also establish the nonexistence results of nontrivial solutions to the problem.

Keywords

• <i>p</i>-Laplacian
• multiplicity of positive solutions
• exterior domain