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

Honghui Yin ; Zuodong Yang

Annales Polonici Mathematici, Tome 105 (2012), p. 293-308 / Harvested from The Polish Digital Mathematics Library

Résumé

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.

Détail

Publié le : 2012-01-01

Zbl 1258.35091

EUDML-ID : urn:eudml:doc:280185