In this paper we prove the existence and regularity of positive solutions of the homogeneous Dirichlet problem −∆u = g(x, u) in Ω, u = 0 on ∂ Ω, where g(x, u) can be singular as u → 0+ and 0 ≤ g(x, u) ≤ φ0 (x) up or 0 ≤ g(x, u) ≤ φ0 (x)(1 + 1/u^p ), with φ_0∈ L^m(Ω), 1≤ m. There are no assumptions on the monotonicity of g(x, ·) and the existence of super- or sub-solutions.

On a Dirichlet problem in bounded domains with singular nonlinearity

COCLITE, Giuseppe Maria;COCLITE, Mario
2013

Abstract

In this paper we prove the existence and regularity of positive solutions of the homogeneous Dirichlet problem −∆u = g(x, u) in Ω, u = 0 on ∂ Ω, where g(x, u) can be singular as u → 0+ and 0 ≤ g(x, u) ≤ φ0 (x) up or 0 ≤ g(x, u) ≤ φ0 (x)(1 + 1/u^p ), with φ_0∈ L^m(Ω), 1≤ m. There are no assumptions on the monotonicity of g(x, ·) and the existence of super- or sub-solutions.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11586/132070
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