Existence and asymptotic behavior of positive solutions for elliptic systems with nonstandard growth conditions

Honghui Yin, and Zuodong Yang. "Existence and asymptotic behavior of positive solutions for elliptic systems with nonstandard growth conditions." Annales Polonici Mathematici 104.3 (2012): 293-308. <http://eudml.org/doc/280185>.

@article{HonghuiYin2012,
abstract = {Our main purpose is to establish the existence of a positive solution of the system ⎧$-∆_\{p(x)\}u = F(x,u,v)$, x ∈ Ω, ⎨$-∆_\{q(x)\}v = H(x,u,v)$, x ∈ Ω, ⎩u = v = 0, x ∈ ∂Ω, where $Ω ⊂ ℝ^\{N\}$ is a bounded domain with C² boundary, $F(x,u,v) = λ^\{p(x)\}[g(x)a(u) + f(v)]$, $H(x,u,v) = λ^\{q(x\})[g(x)b(v) + h(u)]$, λ > 0 is a parameter, p(x),q(x) are functions which satisfy some conditions, and $-∆_\{p(x)\}u = -div(|∇u|^\{p(x)-2\}∇u)$ is called the p(x)-Laplacian. We give existence results and consider the asymptotic behavior of solutions near the boundary. We do not assume any symmetry conditions on the system.},
author = {Honghui Yin, Zuodong Yang},
journal = {Annales Polonici Mathematici},
keywords = {positive solution; -Laplacian; asymptotic behavior; subsupersolution},
language = {eng},
number = {3},
pages = {293-308},
title = {Existence and asymptotic behavior of positive solutions for elliptic systems with nonstandard growth conditions},
url = {http://eudml.org/doc/280185},
volume = {104},
year = {2012},
}

TY - JOUR
AU - Honghui Yin
AU - Zuodong Yang
TI - Existence and asymptotic behavior of positive solutions for elliptic systems with nonstandard growth conditions
JO - Annales Polonici Mathematici
PY - 2012
VL - 104
IS - 3
SP - 293
EP - 308
AB - Our main purpose is to establish the existence of a positive solution of the system ⎧$-∆_{p(x)}u = F(x,u,v)$, x ∈ Ω, ⎨$-∆_{q(x)}v = H(x,u,v)$, x ∈ Ω, ⎩u = v = 0, x ∈ ∂Ω, where $Ω ⊂ ℝ^{N}$ is a bounded domain with C² boundary, $F(x,u,v) = λ^{p(x)}[g(x)a(u) + f(v)]$, $H(x,u,v) = λ^{q(x})[g(x)b(v) + h(u)]$, λ > 0 is a parameter, p(x),q(x) are functions which satisfy some conditions, and $-∆_{p(x)}u = -div(|∇u|^{p(x)-2}∇u)$ is called the p(x)-Laplacian. We give existence results and consider the asymptotic behavior of solutions near the boundary. We do not assume any symmetry conditions on the system.
LA - eng
KW - positive solution; -Laplacian; asymptotic behavior; subsupersolution
UR - http://eudml.org/doc/280185
ER -