Positive weak solutions of elliptic Dirichlet problems with singularities in both the dependent and the independent variables
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...
Elmentve itt :
Szerzők: | |
---|---|
Dokumentumtípus: | Folyóirat |
Megjelent: |
2019
|
Sorozat: | Electronic journal of qualitative theory of differential equations
|
Kulcsszavak: | Differenciálegyenlet |
doi: | 10.14232/ejqtde.2019.1.54 |
Online Access: | http://acta.bibl.u-szeged.hu/62278 |
Tartalmi kivonat: | 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. |
---|---|
Terjedelem/Fizikai jellemzők: | 1-17 |
ISSN: | 1417-3875 |