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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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.

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

First available in Project Euclid: 23 March 2016

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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.

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