Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
840515 | Nonlinear Analysis: Theory, Methods & Applications | 2011 | 13 Pages |
Abstract
We consider a nonlinear elliptic problem driven by the pp-Laplacian, where the right hand side nonlinearity exhibits a pp-linear behavior near infinity and the Euler functional of the problem need not be coercive and, in fact, can be indefinite. Using a combination of minimax arguments with truncation techniques and Morse theory, we show that the problem has at least three nontrivial smooth solutions, two of which have a constant sign. Our method of proof uses some results on critical groups and the spectrum of the pp-Laplacian, due to Perera and Dancer–Perera.
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Authors
Nikolaos S. Papageorgiou, Eugénio M. Rocha,