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.
- Homogeneous Dirichlet problem
- Nonlinear diffusion
- Principle of linearized stability
- Upper and lower solutions
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