Resonant Robin problems with indefinite and unbounded potential

Leszek Gasiński and Nikolaos S. Papageorgiou

Mathematische Nachrichten, 2018, vol. 291, issue 5-6, 848-878

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.

Date: 2018
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https://doi.org/10.1002/mana.201600174

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