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Title: Positive solutions for parametric Dirichlet problems with indefinite potential and superdiffusive reaction
Author: Aizicovici, Sergiu
Papageorgiou, Nikolaos S.
Staicu, Vasile
Keywords: Reaction of superdifussive type
Maximum principle
Local minimizer
Mountain pass theorem
Bifurcation type theorem
Indefinite and unbounded potential
Issue Date: 2016
Publisher: Juliusz Schauder Centre for Nonlinear Studies, Nicolaus Copernicus University
Abstract: We consider a parametric semilinear Dirichlet problem driven by the Laplacian plus an indefinite unbounded potential and with a reaction of superdifissive type. Using variational and truncation techniques, we show that there exists a critical parameter value λ_{∗}>0 such that for all λ> λ_{∗} the problem has least two positive solutions, for λ= λ_{∗} the problem has at least one positive solutions, and no positive solutions exist when λ∈(0,λ_{∗}). Also, we show that for λ≥ λ_{∗} the problem has a smallest positive solution.
Peer review: yes
DOI: 10.12775/TMNA.2016.014
ISSN: 1230-3429
Appears in Collections:CIDMA - Artigos
FAAG - Artigos

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