Topological Methods in Nonlinear Analysis

Multiple nodal solutions for semilinear Robin problems with indefinite linear part and concave terms

Nikolaos S. Papageorgiou, Calogero Vetro, and Francesca Vetro

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We consider a semilinear Robin problem driven by Laplacian plus an indefinite and unbounded potential. The reaction function contains a concave term and a perturbation of arbitrary growth. Using a variant of the symmetric mountain pass theorem, we show the existence of smooth nodal solutions which converge to zero in $C^1(\overline{\Omega})$. If the coefficient of the concave term is sign changing, then again we produce a sequence of smooth solutions converging to zero in $C^1(\overline{\Omega})$, but we cannot claim that they are nodal.

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Topol. Methods Nonlinear Anal., Volume 50, Number 1 (2017), 269-286.

First available in Project Euclid: 14 October 2017

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Papageorgiou, Nikolaos S.; Vetro, Calogero; Vetro, Francesca. Multiple nodal solutions for semilinear Robin problems with indefinite linear part and concave terms. Topol. Methods Nonlinear Anal. 50 (2017), no. 1, 269--286. doi:10.12775/TMNA.2017.029.

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