Positive weak solutions of elliptic Dirichlet problems with singularities in both the dependent and the independent variables

Godoy, Tomas and Guerin, Alfredo: Positive weak solutions of elliptic Dirichlet problems with singularities in both the dependent and the independent variables. (2019)

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Abstract

We consider singular problems of the form −∆u = k (·, u) − h (·, u) in Ω, u = 0 on ∂Ω, u > 0 in Ω, where Ω is a bounded C 1,1 domain in Rn , n ≥ 2, h : Ω × [0, ∞) → [0, ∞) and k : Ω × (0, ∞) → [0, ∞) are Carathéodory functions such that h (x, ·) is nondecreasing, and k (x, ·) is nonincreasing and singular at the origin a.e. x ∈ Ω. Additionally, k (·,s) and h (·,s) are allowed to be singular on ∂Ω for s > 0. Under suitable additional hypothesis on h and k, we prove that the stated problem has a unique weak solution u ∈ H1 0 (Ω), and that u belongs to C . The behavior of the solution near ∂Ω is also addressed.

Item Type: Journal
Publication full: Electronic journal of qualitative theory of differential equations
Date: 2019
Number: 54
ISSN: 1417-3875
Page Range: pp. 1-17
DOI: https://doi.org/10.14232/ejqtde.2019.1.54
Uncontrolled Keywords: Differenciálegyenlet
Additional Information: Bibliogr.: p. 15-17. ; összefoglalás angol nyelven
Date Deposited: 2019. Sep. 30. 09:19
Last Modified: 2020. Jul. 29. 12:24
URI: http://acta.bibl.u-szeged.hu/id/eprint/62278

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