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Neumann problems with indefinite and unbounded potential and concave terms

Authors: Nikolaos S. Papageorgiou and Vicenţiu D. Rădulescu
Journal: Proc. Amer. Math. Soc. 143 (2015), 4803-4816
MSC (2010): Primary 35J20; Secondary 35J60, 58E05
Published electronically: April 10, 2015
MathSciNet review: 3391038
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Abstract: We consider a semilinear parametric Neumann problem driven by the negative Laplacian plus an indefinite and unbounded potential. The reaction is asymptotically linear and exhibits a negative concave term near the origin. Using variational methods together with truncation and perturbation techniques and critical groups, we show that for all small values of the parameter the problem has at least five nontrivial solutions, four of which have constant sign.

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Additional Information

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 80302, Jeddah 21589, Saudi Arabia – and – Institute of Mathematics “Simion Stoilow” of the Romanian Academy, P.O. Box 1-764, 014700 Bucharest, Romania

Keywords: Concave nonlinearity, indefinite and unbounded potential, resonance, Harnack inequality, regularity theory, local minimizers
Received by editor(s): February 3, 2014
Received by editor(s) in revised form: August 2, 2014
Published electronically: April 10, 2015
Communicated by: Catherine Sulem
Article copyright: © Copyright 2015 American Mathematical Society