On Positive Solution for a Class of Nonlinear Elliptic Systems with Indefinite Weights

Abstract

We establish the existence of a nontrivial solution of system:  −∆pu = λ a(x)u|u|p−2 + λ′c(x)u|u|α−1|v|β+1 + f in Ω −∆qv = μ b(x)v|v|q−2 + λ′c(x)|u|α+1v|v|β−1 + g in Ω (u, v) ∈W 1,p 0 (Ω)×W 1,q 0 (Ω) under some restrictions on λ, μ, λ′, α, β, f and g. We show this result by a local minimization.

Cite this paper

@inproceedings{Afrouzi2011OnPS, title={On Positive Solution for a Class of Nonlinear Elliptic Systems with Indefinite Weights}, author={G. A. Afrouzi and Somayeh Khademloo and M. Mirzapour}, year={2011} }