Multiple solutions to a Robin problem with indefinite weight and asymmetric reaction

摘要

The existence of two nontrivial smooth solutions to a semilinear Robin problem with indefinite unbounded potential and asymmetric nonlinearity f is established. Both crossing and resonance are allowed. A third nonzero solution exists provided f is C-1. Proofs exploit variational methods, truncation techniques, and Morse theory. (C) 2015 Elsevier Inc. All rights reserved.