Robin problems with general potential and double resonance. (June 2017) - Papageorgiou, Nikolaos S.; Vetro, Calogero; Vetro, Francesca
Abstract: We consider a semilinear elliptic problem with Robin boundary condition and an indefinite and unbounded potential. The reaction term is a Carathéodory function exhibiting linear growth near ± ∞ . We assume that double resonance occurs with respect to any positive spectral interval. Using variational tools and critical groups, we show that the problem has a nontrivial smooth solution.