Skip to main content
SpringerLink
Log in

Stability of Positive Fixed Points of Nonlinear Operators

  • Published:
Positivity Aims and scope Submit manuscript

Abstract

This paper considers the stability of positive fixed points of nonlinear operators under purturbations. Through the use of the Thompson's metric, we obtain the results in ordered Banach spaces by proving the corresponding results in metric spaces first. An application to the existence of periodic solutions for a parametrized system of ordinary differential equations is given.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. D.W. Boyd, and Wong, J.S.W.: On nonlinear contractions, Proc. Amer. Math. Soc. 20(1969), 458–464.

    Google Scholar 

  2. Chen, Y.-Z.: Thompson's metric and mixed monotone operators, J. Math. Appl. 117(1993), 31–37.

    Google Scholar 

  3. Chen, Y.-Z.: Continuation method for a-sublinear mappings, to appear in Proc. Amer. Math. Soc.

  4. Krasnosel'skii, M.A.: Translation along Trajectories of Differential Equations, Amer. Math. Soc. Transl., Vol. 19, Amer. Math. Soc., Providence, 1968.

  5. Krause, U.: A nonlinear extension of the Birkhoff-Jentzsch theorem, J. Math. Anal. Appl. 114(1986), 552–568.

    Google Scholar 

  6. Krause, U.: Positive nonlinear systems: some results and applications, Proceedings of the First World Congress of Nonlinear Analysts 1992, W. de Gruyter, Berlin, 1994.

    Google Scholar 

  7. Nussbaum, R.D.: Iterated Nonlinear Maps and Hilbert's Projective Metric, Mem. Amer.Math. Soc., Vol. 75, No. 391, 1988.

  8. Smith, H.L.: Monotone Dynamical System: An introduction to the Theory of Competitive and Cooperative Systems, AMS Math. Surv. & Monographs 41, Amer. Math. Soc., Providence, 1995.

  9. Smith, H.L. and Waltman, P.: Perturbation of a globally stable steady state, Proc. Amer. Math. Soc. 127(1999), 447–453.

    Google Scholar 

  10. Thompson, A.C.: On certain mappings in a partially ordered vector space, Proc. Amer. Math. Soc. 14(1963), 438–443.

    Google Scholar 

  11. Zeidler, E.: Nonlinear Functional Analysis and its Applications: I. Fixed Point Theorems, Springer-Verlag, New York, 1986.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Computer Science, and Engineering, University of Pittsburgh at Bradford, Bradford, PA, 16701, USA

    Yong-Zhuo Chen

Authors
  1. Yong-Zhuo Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Chen, YZ. Stability of Positive Fixed Points of Nonlinear Operators. Positivity 6, 47–57 (2002). https://doi.org/10.1023/A:1012079817987

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1012079817987

Search

Navigation