Nodal Solutions for Indefinite Robin Problems

Abstract

We consider a semilinear Robin problem driven by the negative Laplacian plus an indefinite, unbounded potential. The reaction term is a Caratheodory function of arbitrary structure outside an interval \([-c,c]\) (\(c>0\)), odd on \([-c,c]\) and concave near zero. Using a variant of the symmetric mountain pass theorem, together with truncation, perturbation and comparison techniques, we show that the problem has a whole sequence \(\{u_n\}_{n\ge 1}\) of distinct nodal solutions converging to zero in \(C^1({\overline{\Omega }})\).