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

摘要

The existence of two nontrivial smooth solutions to a semilinear Robinproblem with indefinite unbounded potential and asymmetric nonlinearity $f$ isestablished. Both crossing and resonance are allowed. A third nonzero solutionexists provided $f$ is $C^1$. Proofs exploit variational methods, truncationtechniques, and Morse theory.