We study Brezis–Nirenberg type theorems for the equation − Delta u + g(x, u) = f (x, u) in Ω, u=0 ,on ∂Ω, where Ω is a bounded domain in RN , g(x, ·) is increasing and f is a dissipative nonlinearity. We apply such theorems for studying existence and multiplicity of positive solutions for the equation − Delta u = u^−q + λu^p in Ω, u = 0 on ∂Ω, where q > 0, p > 1 and λ > 0.
Brezis-Nirenberg type theorems and multiplicity of positive solutions for a singular elliptic problem
SACCON, CLAUDIO;
2008-01-01
Abstract
We study Brezis–Nirenberg type theorems for the equation − Delta u + g(x, u) = f (x, u) in Ω, u=0 ,on ∂Ω, where Ω is a bounded domain in RN , g(x, ·) is increasing and f is a dissipative nonlinearity. We apply such theorems for studying existence and multiplicity of positive solutions for the equation − Delta u = u^−q + λu^p in Ω, u = 0 on ∂Ω, where q > 0, p > 1 and λ > 0.File in questo prodotto:
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