Positivity

, Volume 17, Issue 2, pp 309–332

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

Authors

    • Faculty of Mathematics and Computer ScienceJagiellonian University
  • Nikolaos S. Papageorgiou
    • Department of MathematicsNational Technical University
Open AccessArticle

DOI: 10.1007/s11117-012-0168-6

Cite this article as:
Gasiński, L. & Papageorgiou, N.S. Positivity (2013) 17: 309. doi:10.1007/s11117-012-0168-6

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.

Keywords

p-LaplacianNonlinear strong maximum principlePositive solutionsUnilateral growth restriction

Mathematics Subject Classification (2000)

35J6535J7035J92
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© The Author(s) 2012