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Topological Methods in Nonlinear Analysis

Nonlinear noncoercive Neumann problems with a reaction concave near the origin
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Nonlinear noncoercive Neumann problems with a reaction concave near the origin

Authors

  • Pasquale Candito
  • Giuseppina D'Aguì
  • Nikolaos S. Papageorgiou

Keywords

Concave term, , constant sign solutions, nodal solutions, nonlinear regularity, critical groups

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.

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Published

2016-03-01

How to Cite

1.
CANDITO, Pasquale, D’AGUÌ, Giuseppina and PAPAGEORGIOU, Nikolaos S. Nonlinear noncoercive Neumann problems with a reaction concave near the origin. Topological Methods in Nonlinear Analysis. Online. 1 March 2016. Vol. 47, no. 1, pp. 289 - 317. [Accessed 6 July 2025].
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