Topological Methods in Nonlinear Analysis

Nonlinear noncoercive Neumann problems with a reaction concave near the origin

Pasquale Candito, Giuseppina D'Aguí, and Nikolaos S. Papageorgiou

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Abstract

We consider a nonlinear Neumann problem driven by the $p$-Laplacian with a concave parametric reaction term and an asymptotically linear perturbation. We prove a multiplicity theorem producing five nontrivial solutions all with sign information when the parameter is small. For the semilinear case $(p=2)$ we produce six solutions, but we are unable to determine the sign of the sixth solution. Our approach uses critical point theory, truncation and comparison techniques, and Morse theory.

Article information

Source
Topol. Methods Nonlinear Anal., Volume 47, Number 1 (2016), 289-317.

Dates
First available in Project Euclid: 23 March 2016

Permanent link to this document
https://projecteuclid.org/euclid.tmna/1458740740

Digital Object Identifier
doi:10.12775/TMNA.2016.007

Mathematical Reviews number (MathSciNet)
MR3469058

Zentralblatt MATH identifier
1373.35148

Citation

Candito, Pasquale; D'Aguí, Giuseppina; Papageorgiou, Nikolaos S. Nonlinear noncoercive Neumann problems with a reaction concave near the origin. Topol. Methods Nonlinear Anal. 47 (2016), no. 1, 289--317. doi:10.12775/TMNA.2016.007. https://projecteuclid.org/euclid.tmna/1458740740


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