Topological Methods in Nonlinear Analysis

Strongly resonant Robin problems with idefinite and unbounded potential

Nikolaos S. Papageorgiou and George Smyrlis

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Abstract

We consider a Robin boundary value problem driven by the Laplacian plus an indefinite and unbounded potential. We assume that the reaction term of the equation is resonant with respect to the principal eigenvalue and the resonance is strong. Using primarily variational tools we prove two multiplicity theorems producing respectively two and three nontrivial smooth solutions.

Article information

Source
Topol. Methods Nonlinear Anal., Volume 49, Number 2 (2017), 511-527.

Dates
First available in Project Euclid: 14 March 2017

Permanent link to this document
https://projecteuclid.org/euclid.tmna/1489457026

Digital Object Identifier
doi:10.12775/TMNA.2016.085

Mathematical Reviews number (MathSciNet)
MR3670472

Zentralblatt MATH identifier
06773137

Citation

Papageorgiou, Nikolaos S.; Smyrlis, George. Strongly resonant Robin problems with idefinite and unbounded potential. Topol. Methods Nonlinear Anal. 49 (2017), no. 2, 511--527. doi:10.12775/TMNA.2016.085. https://projecteuclid.org/euclid.tmna/1489457026


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