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Multiple solutions for strongly resonant Robin problems
Author(s) -
Papageorgiou Nikolaos S.,
Vetro Calogero,
Vetro Francesca
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.201600454
Subject(s) - mathematics , multiplicity (mathematics) , eigenvalues and eigenvectors , laplace operator , nonlinear system , principal (computer security) , p laplacian , pure mathematics , mathematical analysis , quantum mechanics , boundary value problem , physics , computer science , operating system
We consider nonlinear (driven by the p ‐Laplacian) and semilinear Robin problems with indefinite potential and strong resonance with respect to the principal eigenvalue. Using variational methods and critical groups, we prove four multiplicity theorems producing up to four nontrivial smooth solutions.