Abstract
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.
Citation
Nikolaos S. Papageorgiou. Calogero Vetro. Francesca Vetro. "Multiple nodal solutions for semilinear Robin problems with indefinite linear part and concave terms." Topol. Methods Nonlinear Anal. 50 (1) 269 - 286, 2017. https://doi.org/10.12775/TMNA.2017.029