Skip to main content
Log in

A note on equilibrium of eventually strongly monotone skew-product semiflows

  • Published:
Acta Mathematicae Applicatae Sinica, English Series Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Arnold, L., Chueshov, I.D. Order-preserving random dynamical systems: equilibria, attractors, applications. Dyn. Stability Systems, 13: 265–280 (1998)

    MATH  MathSciNet  Google Scholar 

  2. Arnold, L., Chueshov, I.D. Cooperative random and stochastic differential equations. Discrete Continuous Dyn. Systems, 7: 1–33 (2001)

    MATH  MathSciNet  Google Scholar 

  3. Chueshov, I. Monotone Random Systems. Theory and Applications, in: Lecture Notes in Mathematics, Vol. 1779, Springer, Berlin, Heidelberg, 2002

    Google Scholar 

  4. Matano, H. Existence of nontrivial unstable sets for equilibriums of strongly order preserving systems. J. Fac. Sci. Univ. Kyoto, 30: 645–673 (1984)

    MATH  MathSciNet  Google Scholar 

  5. 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)

    Article  MATH  MathSciNet  Google Scholar 

  6. Novo, S., Obaya, R. Strictly ordered minimal subsets of a class of convex monotone skew-product semiflows. J. Differential Equations, 196: 249–288 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  7. Smith, H.L. Monotone Dynamical Systems. An Introduction to the Theory of Competitive and Cooperative Systems, Amer. Math. Soc., Providence, RI, 1995

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Xi-liang Li.

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

Reprints 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

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10255-009-8219-x

Keywords

2000 MR Subject Classification

Navigation