Degenerate elliptic equations with singular nonlinearities |
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Authors: | Daniele Castorina Pierpaolo Esposito Berardino Sciunzi |
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Institution: | (1) Dipartimento di Matematica, Università degli Studi “Roma Tre”, Largo S. Leonardo Murialdo, 1-00146 Rome, Italy;(2) Dipartimento di Matematica, Università della Calabria, Via Pietro Bucci, 1-87036 Arcavacata di Rende (CS), Italy |
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Abstract: | The behavior of the “minimal branch” is investigated for quasilinear eigenvalue problems involving the p-Laplace operator, considered in a smooth bounded domain of , 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 ≠ 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.
Authors are partially supported by MIUR, project “Variational methods and nonlinear differential equations”. |
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Keywords: | Mathematics Subject Classification (2000)" target="_blank">Mathematics Subject Classification (2000) 35B35 35B45 35J70 35J60 |
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