Semilinear Neumann problems with indefinite and unbounded potential and crossing nonlinearity

@inproceedings{Papageorgiou2013SemilinearNP,
  title={Semilinear Neumann problems with indefinite and unbounded potential and crossing nonlinearity},
  author={Nikolaos S. Papageorgiou and Vicentiu D. Radulescu},
  year={2013}
}
We consider a semilinear Neumann problem with an indefinite and unbounded potential and an asymmetric reaction that crosses at least the principal eigenvalue of the operator −Δ + βI in H1(Ω), β being the potential function. Using a combination of variational methods, with truncation and perturbation techniques and Morse theory, we prove multiplicity theorems providing precise sign information for all the solutions. 

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