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Positive solutions of nonlinear Robin eigenvalue problems

Authors: Nikolaos S. Papageorgiou and Vicenţiu D. Rădulescu
Journal: Proc. Amer. Math. Soc. 144 (2016), 4913-4928
MSC (2010): Primary 35J66, 35J92
Published electronically: April 20, 2016
MathSciNet review: 3544539
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Abstract: We consider a nonlinear eigenvalue problem driven by the $ p$-
Laplacian with Robin boundary condition. Using variational methods and truncation techniques, we prove a bifurcation-type result describing the set of positive solutions as the positive parameter $ \lambda $ varies. We also produce extremal positive solutions and study their properties.

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Nikolaos S. Papageorgiou
Affiliation: Department of Mathematics, National Technical University, Zografou Campus, Athens 15780, Greece

Vicenţiu D. Rădulescu
Affiliation: Department of Mathematics, Faculty of Sciences, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia — and — Institute of Mathematics “Simion Stoilow” of the Romanian Academy, P.O. Box 1-764, 014700 Bucharest, Romania

Keywords: Superdiffusive reaction, bifurcation type theorem, extremal positive solutions, $p$-Laplacian, nonlinear regularity
Received by editor(s): May 26, 2015
Received by editor(s) in revised form: January 9, 2016, and January 21, 2016
Published electronically: April 20, 2016
Communicated by: Catherine Sulem
Article copyright: © Copyright 2016 American Mathematical Society

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