, Volume 17, Issue 2, pp 309–332

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


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

DOI: 10.1007/s11117-012-0168-6


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.


p-Laplacian Nonlinear strong maximum principle Positive solutions Unilateral growth restriction

Mathematics Subject Classification (2000)

35J65 35J70 35J92


The authors wish to thank the referee for his/her remarks and for bringing to their attention Reference [3].

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© The Author(s) 2012