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Title: Nonlinear resonant periodic problems with concave terms
Author: Aizicovici, Sergiu
Papageorgiou, Nikolaos S.
Staicu, Vasile
Keywords: Critical groups
Ekeland variational principle
Concave term
Strong deformation retract
Homotopy equivalent
Contractible space
Issue Date: 1-Mar-2011
Abstract: We consider a nonlinear periodic problem, driven by the scalar p-Laplacian with a concave term and a Caratheodory perturbation. We assume that this perturbation f (t, x) is (p−1)- linear at ±∞, and resonance can occur with respect to an eigenvalue λm+1, m 2, of the negative periodic scalar p-Laplacian. Using a combination of variational techniques, based on the critical point theory, with Morse theory, we establish the existence of at least three nontrivial solutions. Useful in our considerations is an alternative minimax characterization of λ1 > 0 (the first nonzero eigenvalue) that we prove in this work.
Peer review: yes
DOI: 10.1016/j.jmaa.2010.09.009
ISSN: 0022-247X
Appears in Collections:DMat - Artigos

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