Resonant semilinear Robin problems with a general potential

Nikolaos S. Papageorgiou, Vicenţiu D. Rădulescu, Dušan D. Repovš

Published 2017-10-28Version 1

We consider a semilinear Robin problem driven by the Laplacian plus an indefinite and unbounded potential. The reaction term is a Carath\'eodory function which is resonant with respect to any nonprincipal eigenvalue both at $\pm \infty$ and 0. Using a variant of the reduction method, we show that the problem has at least two nontrivial smooth solutions.