, 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


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.

L. Gasiński’s research has been partially supported by the Ministry of Science and Higher Education of Poland under Grants no. N201 542438 and N201 604640.