Skip to main content

Stability for almost periodic systems

  • Section I
  • Conference paper
  • First Online:
Japan-United States Seminar on Ordinary Differential and Functional Equations

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 243))

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 34.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 46.00
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. C.C. Conley and R.K. Miller, Asymptotic stability without uniform stability: almost periodic coefficients, J. Differential Eqs., 1 (1965), 333–336.

    Article  MathSciNet  MATH  Google Scholar 

  2. W.A. Coppel, Almost periodic properties of ordinary differential equations, Ann. Mat. Pura Appl., 76(1967), 27–49.

    Article  MathSciNet  MATH  Google Scholar 

  3. L.G. Deysach and G.R. Sell, On the existence of almost periodic motions, Michigan Math. J., 12(1965), 87–95.

    Article  MathSciNet  MATH  Google Scholar 

  4. A.M. Fink and P.O. Frederickson, Ultimate boundedness does not imply almost periodicity, J. Differential Eqs., 9(1971), 280–284.

    Article  MathSciNet  MATH  Google Scholar 

  5. J.K. Hale, J.P. LaSalle and Marshall Slemrod, Theory of a general class of dissipative processes, J. Math. Anal. Appl., (to appear).

    Google Scholar 

  6. J. Kato, Uniformly asymptotic stability and total stability, Tohoku Math. J., 22(1970), 254–269.

    Article  MathSciNet  MATH  Google Scholar 

  7. J. Kato and T. Yoshizawa, A relationship between uniformly asymptotic stability and total stability, Funkcialaj Ekvacioj, 12(1970), 233–238.

    MathSciNet  MATH  Google Scholar 

  8. J.L. Massera, Erratum: Contributions to stability theory, Ann. of Math., 68(1958), 202.

    Article  MATH  Google Scholar 

  9. R.K. Miller, Almost periodic differential equations as dynamical systems with applications to the existence of a. p. solutions, J. Differential Eqs., 1(1965), 337–345.

    Article  MathSciNet  MATH  Google Scholar 

  10. F. Nakajima, Existence of quasi-periodic solutions of quasi-periodic systems, to appear.

    Google Scholar 

  11. Z. Opial, Sur une équation différentielle presque-périodique sans solution presque-périodique, Bull. Acad. Polon. Sci. Ser. Sci. Math. Astron. Phys., 9(1961), 673–676.

    MathSciNet  MATH  Google Scholar 

  12. N. Paval, On dissipative systems, Boll. Unione Mat. Italiana, (to appear).

    Google Scholar 

  13. G. Seifert, Stability conditions for the existence of almost-periodic solutions of almost-periodic systems, J. Math. Anal. Appl., 10(1965), 409–418.

    Article  MathSciNet  MATH  Google Scholar 

  14. G. Seifert, Almost periodic solutions for almost periodic systems of ordinary differential equations, J. Differential Eqs., 2(1966), 305–319.

    Article  MathSciNet  MATH  Google Scholar 

  15. G. Seifert, Almost periodic solutions and asymptotic stability, J. Math. Anal. Appl., 21(1968), 136–149.

    Article  MathSciNet  MATH  Google Scholar 

  16. G.R. Sell, Periodic solutions and asymptotic stability, J. Differential Eqs., 2(1966), 143–157.

    Article  MathSciNet  MATH  Google Scholar 

  17. G.R. Sell, Nonautonomous differential equations and topological dynamics. I, II, Trans. Amer. Math. Soc., 127(1967), 241–262, 263–283.

    MathSciNet  MATH  Google Scholar 

  18. T. Yoshizawa, Extreme stability and almost periodic solutions of functional-differential equations, Arch. Rational Mech. Anal., 17(1964), 148–170.

    Article  MathSciNet  MATH  Google Scholar 

  19. T. Yoshizawa, "Stability Theory by Liapunov's Second Method." The Mathematical Society of Japan, Tokyo, 1966.

    MATH  Google Scholar 

  20. T. Yoshizawa, Stability and existence of periodic and almost periodic solutions, Proc. of United States-Japan Seminar on Differential and Functional Equations, 1967, 411–427.

    Google Scholar 

  21. T. Yoshizawa, Stability and existence of a periodic solution, J. Differential Eqs., 4(1968), 121–129.

    Article  MathSciNet  MATH  Google Scholar 

  22. T. Yoshizawa, Some remarks on the existence and the stability of almost periodic solutions, Studies in Applied Mathematics, 5 (1969), 166–172.

    MathSciNet  Google Scholar 

  23. T. Yoshizawa, Asymptotically almost periodic solutions of an almost periodic system, Funkcialaj Ekvacioj, 12(1969), 23–40.

    MathSciNet  MATH  Google Scholar 

Download references

Authors

Editor information

Minoru Urabe

Rights and permissions

Reprints and permissions

Copyright information

© 1971 Springer-Verlag

About this paper

Cite this paper

Yoshizawa, T. (1971). Stability for almost periodic systems. In: Urabe, M. (eds) Japan-United States Seminar on Ordinary Differential and Functional Equations. Lecture Notes in Mathematics, vol 243. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0058716

Download citation

  • DOI: https://doi.org/10.1007/BFb0058716

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-05708-6

  • Online ISBN: 978-3-540-37080-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics