, Volume 17, Issue 2, pp 309–332 | Cite as

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

Open Access


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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Copyright information

© The Author(s) 2012

Authors and Affiliations

  1. 1.Faculty of Mathematics and Computer ScienceJagiellonian UniversityKrakówPoland
  2. 2.Department of MathematicsNational Technical UniversityAthensGreece

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