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Title: Constant sign and nodal solutions for nonlinear elliptic equations with combined nonlinearities
Author: Aizicovici, S.
Papageorgiou, N. S.
Staicu, V.
Keywords: Nodal solutions
Nonlinear regularity
Local minimizer
Extremal solutions
Critical groups
Superlinear reaction
Concave term
Issue Date: Jun-2015
Publisher: International Press
Abstract: We study a parametric nonlinear Dirichlet problem driven by a nonhomogeneous differential operator and with a reaction which is ”concave” (i.e., (p − 1)− sublinear) near zero and ”convex” (i.e., (p − 1)− superlinear) near ±1. Using variational methods combined with truncation and comparison techniques, we show that for all small values of the parameter > 0, the problem has at least five nontrivial smooth solutions (four of constant sign and the fifth nodal). In the Hilbert space case (p = 2), using Morse theory, we produce a sixth nontrivial smooth solution but we do not determine its sign.
Peer review: yes
DOI: 10.4310/MAA.2015.v22.n2.a5
ISSN: 1073-2772
Appears in Collections:CIDMA - Artigos
FAAG - Artigos

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