Existence of nontrivial unstable sets for equilibriums of strongly order- preserving systems. (English) Zbl 0545.35042

The author shows that for a certain class of semi-dynamical systems (namely those strongly order-preserving systems that satisfy a certain compactness condition), any unstable equilibrium point has a non-trivial unstable set. Such systems include, for example, certain reaction- diffusion systems. The existence of an orbit connecting a pair of neighbouring equilibrium solutions and a criterion for the existence of a stable equilibrium solution are also established.
Reviewer: Simeon Reich


35G10 Initial value problems for linear higher-order PDEs
35K25 Higher-order parabolic equations
37-XX Dynamical systems and ergodic theory
35B35 Stability in context of PDEs