We study the Dirichlet boundary value problem $$-\Delta u=\frac{\lambda f(x)}{(1-u)^2}$$ on a bounded domain Ω ⊂ ℝ^N. For 2 ≤ N ≤ 7, we characterize compactness for solutions sequence in terms of spectral informations. As a by-product, we give an uniqueness result for λ close to 0 and λ* in the class of all solutions with finite Morse index, λ* being the extremal value associated to the nonlinear eigenvalue problem.
Esposito, P. (2008). Compactness of a nonlinear eigenvalue problem with a singular nonlinearity. COMMUNICATIONS IN CONTEMPORARY MATHEMATICS, 10(1), 1-29 [10.1142/S0219199708002697].
Compactness of a nonlinear eigenvalue problem with a singular nonlinearity
ESPOSITO, PIERPAOLO
2008-01-01
Abstract
We study the Dirichlet boundary value problem $$-\Delta u=\frac{\lambda f(x)}{(1-u)^2}$$ on a bounded domain Ω ⊂ ℝ^N. For 2 ≤ N ≤ 7, we characterize compactness for solutions sequence in terms of spectral informations. As a by-product, we give an uniqueness result for λ close to 0 and λ* in the class of all solutions with finite Morse index, λ* being the extremal value associated to the nonlinear eigenvalue problem.File in questo prodotto:
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