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

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 C1(Ω). If the coefficient of the concave term is sign changing, then again we produce a sequence of smooth solutions converging to zero in C1(Ω), but we cannot claim that they are nodal.