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Resonant Robin problems with indefinite and unbounded potential

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  • Leszek GasiÅ„ski
  • Nikolaos S. Papageorgiou

Abstract

We consider semilinear elliptic problems with an indefinite and unbounded potential and Robin boundary condition. We prove existence and multiplicity theorems when resonance occurs with respect to the principal eigenvalue λ̂1 both from the left and from the right. We also investigate the case where we have resonance with respect to any nonprincipal eigenvalue and prove a multiplicity theorem under general conditions on the reaction term f(z,ζ). Our approach uses variational methods, together with truncation and perturbation techniques and Morse theory.

Suggested Citation

  • Leszek GasiÅ„ski & Nikolaos S. Papageorgiou, 2018. "Resonant Robin problems with indefinite and unbounded potential," Mathematische Nachrichten, Wiley Blackwell, vol. 291(5-6), pages 848-878, April.
    • Handle: RePEc:bla:mathna:v:291:y:2018:i:5-6:p:848-878
    DOI: 10.1002/mana.201600174
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