Multiplicity of solutions for resonant Neumann problems with an indefinite and unbounded potential
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- by Nikolaos S. Papageorgiou and Vicenţiu D. Rădulescu PDF
- Trans. Amer. Math. Soc. 367 (2015), 8723-8756 Request permission
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).References
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Additional Information
- Nikolaos S. Papageorgiou
- Affiliation: Department of Mathematics, Zografou Campus, National Technical University, Athens 15780, Greece
- MR Author ID: 135890
- 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
- MR Author ID: 143765
- ORCID: 0000-0003-4615-5537
- Email: vicentiu.radulescu@math.cnrs.fr
- Received by editor(s): December 20, 2013
- Published electronically: November 6, 2014
- © Copyright 2014 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 367 (2015), 8723-8756
- MSC (2010): Primary 35J20, 35J60, 58E05
- DOI: https://doi.org/10.1090/S0002-9947-2014-06518-5
- MathSciNet review: 3403070