, Volume 17, Issue 2, pp 309-332

First online:

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

  • Leszek GasińskiAffiliated withFaculty of Mathematics and Computer Science, Jagiellonian University Email author 
  • , Nikolaos S. PapageorgiouAffiliated withDepartment of Mathematics, National Technical University


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