Skip to main content
SpringerLink
Log in

On the classes of differential systems with the desired behavior

  • Published:
Rendiconti del Circolo Matematico di Palermo Aims and scope Submit manuscript

Summary

A discussion of the affect of perturbations on systems of differential equations is presented. In particular, given a property of the solutions of a differential system, we are interested in finding a class of differential equations related to the original system that have a certain prescribed property. Lyapunov theory is the main technique employed.

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. S. Bernfeld,The extendability of solutions of perturbed scalar differential equations, to appear in Pacific J. of Math.

  2. C. Corduneanu,Sur la construction des fonctions de Liapounoff, Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys. 10 (1962), 559–563.

    MATH  MathSciNet  Google Scholar 

  3. J. Kurzweil,On the reversibility of the first theorem of Liapunov concerning the stability of motion, Czechoslovak Math. J. 5 (1955), 382–398.

    MathSciNet  Google Scholar 

  4. V. Lakshmikantham and S. Leela,On the Construction of Lyapunov functions, Rev. Math. Pures Appl. 12 (1967), 969–976.

    MATH  MathSciNet  Google Scholar 

  5. V. Lakshmikantham and S. Leela,Differential and Integral Inequalities, Vol. I, Academic Press, New York, 1969.

    MATH  Google Scholar 

  6. T. Yoshizawa,Liapunov’s function and boundedness of solutions, Funkciala, Ekvacioj, 2 (1959), 95–142.

    MATH  MathSciNet  Google Scholar 

  7. T. Yoshizawa,The stability theory by Liapunov’s second method, Math. Soc. Japan, Tokyo, 1967.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Kingston, U.S.A.

    S. Bernfeld, G. Ladde & V. Lakshmikantham

Authors
  1. S. Bernfeld
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. G. Ladde
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. V. Lakshmikantham
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Introduced by G. Sansone.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bernfeld, S., Ladde, G. & Lakshmikantham, V. On the classes of differential systems with the desired behavior. Rend. Circ. Mat. Palermo 21, 85–97 (1972). https://doi.org/10.1007/BF02844234

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02844234

Keywords

Search

Navigation