Please use this identifier to cite or link to this item:
http://hdl.handle.net/10773/14988
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 |
URI: | http://hdl.handle.net/10773/14988 |
DOI: | 10.4310/MAA.2015.v22.n2.a5 |
ISSN: | 1073-2772 |
Appears in Collections: | CIDMA - Artigos FAAG - Artigos |
Files in This Item:
File | Description | Size | Format | |
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P65_MAA_22(2015)_221-248.pdf | Main article | 266.66 kB | Adobe PDF | View/Open |
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