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.
Citation
Pasquale Candito. Giuseppina D'Aguí. Nikolaos S. Papageorgiou. "Nonlinear noncoercive Neumann problems with a reaction concave near the origin." Topol. Methods Nonlinear Anal. 47 (1) 289 - 317, 2016. https://doi.org/10.12775/TMNA.2016.007
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