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

Nikolaos S. Papageorgiou, Calogero Vetro, Francesca Vetro



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.


Indefinite potential; nodal solutions; extremal constant sign solutions; regularity theory; concave term

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