Existence of positive radial solutions for the elliptic equations on an exterior domain

Yongxiang Li, and Huanhuan Zhang. "Existence of positive radial solutions for the elliptic equations on an exterior domain." Annales Polonici Mathematici 116.1 (2016): 67-78. <http://eudml.org/doc/280889>.

@article{YongxiangLi2016,
abstract = {We discuss the existence of positive radial solutions of the semilinear elliptic equation ⎧-Δu = K(|x|)f(u), x ∈ Ω ⎨αu + β ∂u/∂n = 0, x ∈ ∂Ω, ⎩$lim_\{|x|→∞\} u(x) = 0$, where $Ω = \{x ∈ ℝ^\{N\}: |x| > r₀\}$, N ≥ 3, K: [r₀,∞) → ℝ⁺ is continuous and $0 < ∫_\{r₀\}^\{∞\} rK(r)dr < ∞$, f ∈ C(ℝ⁺,ℝ⁺), f(0) = 0. Under the conditions related to the asymptotic behaviour of f(u)/u at 0 and infinity, the existence of positive radial solutions is obtained. Our conditions are more precise and weaker than the superlinear or sublinear growth conditions. Our discussion is based on the fixed point index theory in cones.},
author = {Yongxiang Li, Huanhuan Zhang},
journal = {Annales Polonici Mathematici},
keywords = {elliptic equation; positive radial solution; exterior domain; cone; fixed point index},
language = {eng},
number = {1},
pages = {67-78},
title = {Existence of positive radial solutions for the elliptic equations on an exterior domain},
url = {http://eudml.org/doc/280889},
volume = {116},
year = {2016},
}

TY - JOUR
AU - Yongxiang Li
AU - Huanhuan Zhang
TI - Existence of positive radial solutions for the elliptic equations on an exterior domain
JO - Annales Polonici Mathematici
PY - 2016
VL - 116
IS - 1
SP - 67
EP - 78
AB - We discuss the existence of positive radial solutions of the semilinear elliptic equation ⎧-Δu = K(|x|)f(u), x ∈ Ω ⎨αu + β ∂u/∂n = 0, x ∈ ∂Ω, ⎩$lim_{|x|→∞} u(x) = 0$, where $Ω = {x ∈ ℝ^{N}: |x| > r₀}$, N ≥ 3, K: [r₀,∞) → ℝ⁺ is continuous and $0 < ∫_{r₀}^{∞} rK(r)dr < ∞$, f ∈ C(ℝ⁺,ℝ⁺), f(0) = 0. Under the conditions related to the asymptotic behaviour of f(u)/u at 0 and infinity, the existence of positive radial solutions is obtained. Our conditions are more precise and weaker than the superlinear or sublinear growth conditions. Our discussion is based on the fixed point index theory in cones.
LA - eng
KW - elliptic equation; positive radial solution; exterior domain; cone; fixed point index
UR - http://eudml.org/doc/280889
ER -