Positivity

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

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

Open Access
Article

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-Laplacian Nonlinear strong maximum principle Positive solutions Unilateral growth restriction 

Mathematics Subject Classification (2000)

35J65 35J70 35J92 

Notes

Acknowledgments

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

Open Access

This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution, and reproduction in any medium, provided the original author(s) and the source are credited.

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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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