A Remark on the Linearized Stability of Positive Solutions for Systems Involving the p-Laplacian

The aim of this paper is to prove some stability result for nonlinear elliptic systems of the form where Δ_p denotes the p-Laplacian operator defined by Δ_pz = div(|∇ z|^p-2∇ z); p > 2, Ω is a bounded domain in R^N (N > 1) with smooth boundary where with h = 1 when α = 1, λ is a positive parameter and f,g are C² functin on 0,∞) × 0,∞). We prove stability and instability results of positive stationary solutions under various choices of f and g.