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2017 Robin problems with indefinite and unbounded potential, resonant at $-\infty$, superlinear at $+\infty$
Nikolaos S. Papageorgiou, Vicenţiu D. Rădulescu
Tohoku Math. J. (2) 69(2): 261-286 (2017). DOI: 10.2748/tmj/1498269626

Abstract

We consider a semilinear Robin problem with an indefinite and unbounded potential and a reaction which exhibits asymmetric behavior as $x\rightarrow\pm\infty$. More precisely it is sublinear near $-\infty$ with possible resonance with respect to the principal eigenvalue of the negative Robin Laplacian and it is superlinear at $+\infty$. Resonance is also allowed at zero with respect to any nonprincipal eigenvalue. We prove two multiplicity results. In the first one, we obtain two nontrivial solutions and in the second, under stronger regularity conditions on the reaction, we produce three nontrivial solutions. Our work generalizes the recent one by Recova-Rumbos (Nonlin. Anal. 112 (2015), 181--198).

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Nikolaos S. Papageorgiou. Vicenţiu D. Rădulescu. "Robin problems with indefinite and unbounded potential, resonant at $-\infty$, superlinear at $+\infty$." Tohoku Math. J. (2) 69 (2) 261 - 286, 2017. https://doi.org/10.2748/tmj/1498269626

Information

Published: 2017
First available in Project Euclid: 24 June 2017

zbMATH: 1375.35202
MathSciNet: MR3682166
Digital Object Identifier: 10.2748/tmj/1498269626

Subjects:
Primary: 35J20
Secondary: 35J60, 58E05

Rights: Copyright © 2017 Tohoku University

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Vol.69 • No. 2 • 2017
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