Existence and nonexistence of solutions for a quasilinear elliptic system

Qin Li, and Zuodong Yang. "Existence and nonexistence of solutions for a quasilinear elliptic system." Annales Polonici Mathematici 113.2 (2015): 155-164. <http://eudml.org/doc/280748>.

@article{QinLi2015,
abstract = {By a sub-super solution argument, we study the existence of positive solutions for the system ⎧$-Δ_\{p\}u = a₁(x)F₁(x,u,v)$ in Ω, ⎪$-Δ_\{q\}v = a₂(x)F₂(x,u,v)$ in Ω, ⎨u,v > 0 in Ω, ⎩u = v = 0 on ∂Ω, where Ω is a bounded domain in $ℝ^\{N\}$ with smooth boundary or $Ω = ℝ^\{N\}$. A nonexistence result is obtained for radially symmetric solutions.},
author = {Qin Li, Zuodong Yang},
journal = {Annales Polonici Mathematici},
keywords = {quasilinear elliptic system; existence; nonexistence; sub-super solution},
language = {eng},
number = {2},
pages = {155-164},
title = {Existence and nonexistence of solutions for a quasilinear elliptic system},
url = {http://eudml.org/doc/280748},
volume = {113},
year = {2015},
}

TY - JOUR
AU - Qin Li
AU - Zuodong Yang
TI - Existence and nonexistence of solutions for a quasilinear elliptic system
JO - Annales Polonici Mathematici
PY - 2015
VL - 113
IS - 2
SP - 155
EP - 164
AB - By a sub-super solution argument, we study the existence of positive solutions for the system ⎧$-Δ_{p}u = a₁(x)F₁(x,u,v)$ in Ω, ⎪$-Δ_{q}v = a₂(x)F₂(x,u,v)$ in Ω, ⎨u,v > 0 in Ω, ⎩u = v = 0 on ∂Ω, where Ω is a bounded domain in $ℝ^{N}$ with smooth boundary or $Ω = ℝ^{N}$. A nonexistence result is obtained for radially symmetric solutions.
LA - eng
KW - quasilinear elliptic system; existence; nonexistence; sub-super solution
UR - http://eudml.org/doc/280748
ER -