Existence of positive solutions to singular elliptic problems with gradient terms
- 1Univ. of Lodz, Poland
Abstract
In this article, we study the existence of classical, positive solutions that vanish asymptotically at infinity to the class of singular elliptic problems with equation Δ u(x)+f(x,u(x))−b(x)(u(x))−1|∇ u(x)|2+g(x)x·∇ u(x)=0 in the exterior domain denoted by ΩR={x∈ℝn,|x| >R >1}, n >2. Moreover, we study the problem with additional boundary condition u(x) = S when |x|=R. In the first part of the paper, we present auxiliary results concerning existence and multiplicity of solutions for the case when b≡0. These results play a crucial role in the proof of the existence of solution for our singular problem in the second part of this paper. We base our approach on the sub-super solution method for bounded sub-domains, as well as the approximation method for the unbounded domain combined with some classical convergence procedure.
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BibTeX
@article{garbowski2026existence,
title = {{Existence of positive solutions to singular elliptic problems with gradient terms}},
author = {Krzysztof Garbowski},
journal = {Electronic Journal of Differential Equations},
year = {2026},
month = oct,
url = {http://ejde.math.txstate.edu/Volumes/2026/81/abstr.html},
note = {CC BY},
}
RIS
TY - JOUR
TI - Existence of positive solutions to singular elliptic problems with gradient terms
AU - Krzysztof Garbowski
PY - 2026
DA - 2026/10/23
JO - Electronic Journal of Differential Equations
UR - http://ejde.math.txstate.edu/Volumes/2026/81/abstr.html
AB - In this article, we study the existence of classical, positive solutions that vanish asymptotically at infinity to the class of singular elliptic problems with equation Δ u(x)+f(x,u(x))−b(x)(u(x))^−1|∇ u(x)|^2+g(x)x·∇ u(x)=0 in the exterior domain denoted by Ω_R={x∈ℝ^n,|x| >R >1}, n >2. Moreover, we study the problem with additional boundary condition u(x) = S when |x|=R. In the first part of the paper, we present auxiliary results concerning existence and multiplicity of solutions for the case when b≡0. These results play a crucial role in the proof of the existence of solution for our singular problem in the second part of this paper. We base our approach on the sub-super solution method for bounded sub-domains, as well as the approximation method for the unbounded domain combined with some classical convergence procedure.
SN - 1072-6691
ER -