Please use this identifier to cite or link to this item:
http://hdl.handle.net/10773/41631
Title: | Pairs of positive solutions for p-Laplacian equations with sublinear and superlinear nonlinearities which do not satisfy the AR-condition |
Author: | Papageorgiou, Nikolaos S. Rocha, Eugénio M. |
Keywords: | p-Laplacian (p−1)-superlinear nonlinearity Positive solutions Cerami condition Ekeland variational principle Mountain pass theorem Ambrosetti–Rabinowitz condition |
Issue Date: | 2009 |
Publisher: | Elsevier |
Abstract: | We consider a nonlinear Dirichlet problem driven by the p-Laplacian differential. The righthand-side nonlinearity, exhibits a (p − 1)-sublinear term of the form m(z)|x| r−2 x, r < p (concave term), and a Carathéodory term f(z, x) which is (p − 1)-superlinear near +∞. However, it does not satisfy the usual Ambrosetti–Rabinowitz condition (AR-condition). Instead we employ a more general condition. Using a variational approach based on the critical point theory and the Ekeland variational principle, we show the existence of two nontrivial positive smooth solutions and then the existence of two nontrivial negative smooth solutions. |
Peer review: | yes |
URI: | http://hdl.handle.net/10773/41631 |
DOI: | 10.1016/j.na.2008.07.042 |
ISSN: | 0362-546X |
Appears in Collections: | CIDMA - Artigos FAAG - Artigos |
Files in This Item:
File | Description | Size | Format | |
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1-s2.0-S0362546X08004380-main.pdf | 562.84 kB | Adobe PDF |
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