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.
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The authors wish to thank the referee for his/her remarks and for bringing to their attention Reference [3].
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L. Gasiński’s research has been partially supported by the Ministry of Science and Higher Education of Poland under Grants no. N201 542438 and N201 604640.
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Gasiński, L., Papageorgiou, N.S. Existence and uniqueness of positive solutions for the Neumann p-Laplacian. Positivity 17, 309–332 (2013). https://doi.org/10.1007/s11117-012-0168-6
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DOI: https://doi.org/10.1007/s11117-012-0168-6