Instability of Positive Solutions for Population Models Involving the p-Laplacian Operator

We study the stability of positive solution to the boundary value problem where Δ_p denotes the p-Laplacian operator defined by is a bounded domain in R^N (N ≥ 1) with ∂Ω of class C^1,β for β ∈ (0, 1) and connected (if N = 1, we assume Ω is bounded open interval), λ > 0, and the weight m(x) satisfies m(x) ∈ C(Ω), m(x) ≥ m₀ > 0 for all x ∈ Ω. We shall establish that every positive solution is lineary unstable.