Upper and Lower Solutions for a Homogeneous Dirichlet Problem with Nonlinear Diffusion and the Principle of Linearized Stability
Robert Stephen Cantrell, Chris Cosner · Rocky Mountain Journal of Mathematics · 2000
We consider a class of quasilinear elliptic equations on a bounded domain subject to homogeneous Dirichlet boundary data.We establish a means of constructing upper and lower solutions in a neighborhood of a given solution to the quasilinear boundary value problem, leading to a principle of linearized stability instability for the solution viewed as an equilibrium to the corresponding parabolic problem.