Matano, Hiroshi Existence of nontrivial unstable sets for equilibriums of strongly order- preserving systems. (English) Zbl 0545.35042 J. Fac. Sci., Univ. Tokyo, Sect. I A 30, 645-673 (1984). 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 Cited in 4 ReviewsCited in 75 Documents MSC: 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 Keywords:semi-dynamical systems; order-preserving systems; compactness; unstable equilibrium point; non-trivial unstable set; reaction-diffusion; existence; stable equilibrium solution PDFBibTeX XMLCite \textit{H. Matano}, J. Fac. Sci., Univ. Tokyo, Sect. I A 30, 645--673 (1984; Zbl 0545.35042)