Instability Criteria for Solutions of Second Order Elliptic Quasilinear Differential Equations

Let Ω ⊂ R ⁿ be a bounded domain with smooth boundary ∂Ω and suppose that v: Ω → R satisfies an elliptic differential equation, e.g. 1 − ∇ v = f ( x , v )   in   Ω https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203744369/d9858e60-9246-4876-bb34-38e3d28ecc5f/content/eq1341.tif"/>