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EnglishThe behavior of the "minimal branch" is investigated for quasilinear eigenvalue problems involving the p-Laplace operator, considered in a smooth bounded domain of R-N, and compactness holds below a critical dimension N-#. The nonlinearity f (u) lies in a very general class and the results we present are new even for p = 2. Due to the degeneracy of p-Laplace operator, for p not equal 2 it is crucial to define a suitable notion of semi-stability: the functional space we introduce in the paper seems to be the natural one and yields to a spectral theory for the linearized operator. For the case p = 2, compactness is also established along unstable branches satisfying suitable spectral information. The analysis is based on a blow-up argument and stronger assumptions on the nonlinearity f (u) are required.
Degenerate elliptic equations with singular nonlinearities / Castorina, D; Esposito, P; Sciunzi, Berardino. - In: CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS. - ISSN 0944-2669. - 34:3(2009), pp. 279-306.
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| Titolo: | Degenerate elliptic equations with singular nonlinearities |
| Autori: | |
| Data di pubblicazione: | 2009 |
| Rivista: | |
| Citazione: | Degenerate elliptic equations with singular nonlinearities / Castorina, D; Esposito, P; Sciunzi, Berardino. - In: CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS. - ISSN 0944-2669. - 34:3(2009), pp. 279-306. |
| Handle: | http://hdl.handle.net/20.500.11770/132684 |
| Appare nelle tipologie: | 1.1 Articolo in rivista |
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