Abstract
In this paper, we show that for an eventually strongly monotone skew-product semiflow τ, the strict ordering on E c (the set consisting of continuous equilibria of τ) implies the strong one.
Similar content being viewed by others
References
Arnold, L., Chueshov, I.D. Order-preserving random dynamical systems: equilibria, attractors, applications. Dyn. Stability Systems, 13: 265–280 (1998)
Arnold, L., Chueshov, I.D. Cooperative random and stochastic differential equations. Discrete Continuous Dyn. Systems, 7: 1–33 (2001)
Chueshov, I. Monotone Random Systems. Theory and Applications, in: Lecture Notes in Mathematics, Vol. 1779, Springer, Berlin, Heidelberg, 2002
Matano, H. Existence of nontrivial unstable sets for equilibriums of strongly order preserving systems. J. Fac. Sci. Univ. Kyoto, 30: 645–673 (1984)
Novo, S., Núñez, C., Obaya, R. Almost automorphic and almost periodic dynamics for quasimonotone nonautonomous functional differential equations. J. Dynam. Differential Equations, 17(3): 589–619 (2005)
Novo, S., Obaya, R. Strictly ordered minimal subsets of a class of convex monotone skew-product semiflows. J. Differential Equations, 196: 249–288 (2004)
Smith, H.L. Monotone Dynamical Systems. An Introduction to the Theory of Competitive and Cooperative Systems, Amer. Math. Soc., Providence, RI, 1995
Author information
Authors and Affiliations
Corresponding author
Additional information
Partially supported by the National Basic Research Program of China, 973 Project (No. 2005CB321902) and the Key Lab of Random Complex Structures and Data Science, CAS.
Rights and permissions
About this article
Cite this article
Li, Xl., Zheng, Zh. A note on equilibrium of eventually strongly monotone skew-product semiflows. Acta Math. Appl. Sin. Engl. Ser. 26, 307–310 (2010). https://doi.org/10.1007/s10255-009-8219-x
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10255-009-8219-x