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, M.. - In: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. - ISSN 1078-0947. - 33:11-12(2013), pp. 4923-4944. [10.3934/dcds.2013.33.4923]
On a Dirichlet problem in bounded domains with singular nonlinearity
COCLITE, Giuseppe Maria;
2013-01-01
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.File in questo prodotto:
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