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Transactions of the American Mathematical Society

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Multiplicity of solutions for resonant Neumann problems with an indefinite and unbounded potential


Authors: Nikolaos S. Papageorgiou and Vicenţiu D. Rădulescu
Journal: Trans. Amer. Math. Soc. 367 (2015), 8723-8756
MSC (2010): Primary 35J20, 35J60, 58E05
Published electronically: November 6, 2014
MathSciNet review: 3403070
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Abstract: We examine semilinear Neumann problems driven by the Laplacian plus an unbounded and indefinite potential. The reaction is a Carathéodory function which exhibits linear growth near $ \pm \infty $. We allow for resonance to occur with respect to a nonprincipal nonnegative eigenvalue, and we prove several multiplicity results. Our approach uses critical point theory, Morse theory and the reduction method (the Lyapunov-Schmidt method).


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Additional Information

Nikolaos S. Papageorgiou
Affiliation: Department of Mathematics, Zografou Campus, National Technical University, Athens 15780, Greece
Email: npapg@math.ntua.gr

Vicenţiu D. Rădulescu
Affiliation: Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia — and — Institute of Mathematics “Simion Stoilow” of the Romanian Academy, P.O. Box 1-764, 014700 Bucharest, Romania
Email: vicentiu.radulescu@math.cnrs.fr

DOI: https://doi.org/10.1090/S0002-9947-2014-06518-5
Keywords: Indefinite and unbounded potential, reduction method, resonance, unique continuation property, regularity, critical groups
Received by editor(s): December 20, 2013
Published electronically: November 6, 2014
Article copyright: © Copyright 2014 American Mathematical Society