, Volume 17, Issue 2, pp 309-332,
Open Access This content is freely available online to anyone, anywhere at any time.
Date: 04 Mar 2012

Existence and uniqueness of positive solutions for the Neumann p -Laplacian

Abstract

We consider a nonlinear Neumann problem driven by the p-Laplacian and with a Carathéodory reaction which satisfies only a unilateral growth restriction. Using the principal eigenvalue of an eigenvalue problem involving the Neumann p-Laplacian plus an indefinite potential, we produce necessary and sufficient conditions for the existence and uniqueness of positive smooth solutions.