Stability properties of non-negative solutions to a non-autonomous p-Laplacian equation

We study the stability of non-negative stationary solutions of

where Δ_p denotes the p-Laplacian operator defined by Δ_pz = div(z^p?2z); p > 2, Ω is a bounded domain in R^N(N  1) with smooth boundary where 0,1],h:?Ω→R⁺ with h = 1 when  = 1, λ > 0, and g:Ω×0,∞)→R is a continuous function. If g(x, u)/u^p?1 be strictly increasing (decreasing), we provide a simple proof to establish that every non-trivial non-negative solution is unstable (stable).