Existence and uniqueness of positive solutions for the Neumann p-Laplacian
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- Gasiński, L. & Papageorgiou, N.S. Positivity (2013) 17: 309. doi:10.1007/s11117-012-0168-6
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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.