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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

Convergence of monotone dynamical systems with minimal equilibria


Author: Jian Hong Wu
Journal: Proc. Amer. Math. Soc. 106 (1989), 907-911
MSC: Primary 58F32; Secondary 34K25, 58D25, 92A09, 92A15
MathSciNet review: 1004632
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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.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1989-1004632-7
PII: S 0002-9939(1989)1004632-7
Article copyright: © Copyright 1989 American Mathematical Society