Convergence of monotone dynamical systems with minimal equilibria

Wu, Jian Hong

doi:10.1090/S0002-9939-1989-1004632-7

Convergence of monotone dynamical systems with minimal equilibria
HTML articles powered by AMS MathViewer

by Jian Hong Wu PDF

Proc. Amer. Math. Soc. 106 (1989), 907-911 Request permission

Abstract:

We show that each precompact orbit of strongly monotone dynamical systems on a Banach lattice $X$ is convergent if there is a continuous map $e:X \to E$, the set of equilibria, such that $e(x)$ is the maximal element in $E$ with $e(x) \leq x$. This result can be applied to study the convergence of a class of functional differential equations and partial differential equations.

References

István Győri, Connections between compartmental systems with pipes and integro-differential equations, Math. Modelling 7 (1986), no. 9-12, 1215–1238. Mathematical models in medicine: diseases and epidemics, Part 2. MR 877750, DOI 10.1016/0270-0255(86)90077-1

On stabilization of discrete strongly order-preserving semigroups and dynamical processes

Morris W. Hirsch, Stability and convergence in strongly monotone dynamical systems, J. Reine Angew. Math. 383 (1988), 1–53. MR 921986, DOI 10.1515/crll.1988.383.1
Xavier Mora, Semilinear parabolic problems define semiflows on $C^{k}$ spaces, Trans. Amer. Math. Soc. 278 (1983), no. 1, 21–55. MR 697059, DOI 10.1090/S0002-9947-1983-0697059-8
Hal Smith, Monotone semiflows generated by functional-differential equations, J. Differential Equations 66 (1987), no. 3, 420–442. MR 876806, DOI 10.1016/0022-0396(87)90027-1

Monotone semiflows on product spaces and active compartmental systems with pipes