The Krasnosel'skiĭ-Quittner formula and instability of a reaction-diffusion system with unilateral obstacles

Variational and other types of inequalities involving nonlinear operators (general) (47J20) Monotone operators and generalizations (47H05) Stability in context of PDEs (35B35) Reaction-diffusion equations (35K57) Degree theory for nonlinear operators (47H11) Stability of solutions to ordinary differential equations (34D20) Nonlinear evolution equations (47J35) Unilateral problems for nonlinear parabolic equations and variational inequalities with nonlinear parabolic operators (35K86) Unilateral problems for parabolic systems and systems of variational inequalities with parabolic operators (35K87)