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Resonant Robin problems with indefinite and unbounded potential
Author(s) -
Gasiński Leszek,
Papageorgiou Nikolaos S.
Publication year - 2018
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201600174
Subject(s) - mathematics , eigenvalues and eigenvectors , multiplicity (mathematics) , truncation (statistics) , perturbation (astronomy) , robin boundary condition , boundary value problem , morse theory , mountain pass theorem , mathematical analysis , pure mathematics , mixed boundary condition , nonlinear system , statistics , quantum mechanics , physics
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 eigenvalueλ ̂ 1 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.