Advertisement

Annali di Matematica Pura ed Applicata

, Volume 108, Issue 1, pp 125–135 | Cite as

The invariance of limit sets for retarded differential equations

  • Nicolas Rouche
Article
  • 29 Downloads

Keywords

Differential Equation Ensemble Limites Retarded Differential Equation Ensemble Compact 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Résumé

On démontre la semi-invariance ou la quasi-invariance des ensembles limites pour une équation différentielle à retard, sans supposer l'unicité ni la prolongeabilité des solutions, et sans supposer non plus que la solution engendrant l'ensemble limite soit contenue dans un ensemble compact ou fermé.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliography

  1. [1]
    J.-P. LaSalle,Some extensions of Liapunov's second method, IRE Trans. Circuit Theory, CT-7 (1960), pp. 520–527.Google Scholar
  2. [2]
    J.-P. LaSalle,Stability theory for ordinary differential equations, J. Diff. Equ.,4 (1968), pp. 57–65.CrossRefzbMATHMathSciNetGoogle Scholar
  3. [3]
    P. Hartman,Ordinary differential equations, J. Wiley and Sons, New York (1964).Google Scholar
  4. [4]
    J. L. Corne -N. Rouche,Attractivity of closed sets proved by using a family of Liapunov functions, J. Diff. Equ.,13 (1973), pp. 231–246.CrossRefMathSciNetGoogle Scholar
  5. [5]
    J.-P. LaSalle,Asymptotic stability criteria, Proc. Symp. Appl. Math.,13, pp. 299–307, Amer. Math. Soc., Providence, R. I. (1962).Google Scholar
  6. [6]
    T. Yoshizawa,Asymptotic behavior of solutions of nonlinear differential equations, Contr. Diff. Equ.,1 (1963), pp. 371–387.zbMATHMathSciNetGoogle Scholar
  7. [7]
    R. K. Miller,Asymptotic behavior of solutions of nonlinear differential equations, Trans. Amer. Math. Soc.,115 (1965), pp. 400–416.CrossRefzbMATHMathSciNetGoogle Scholar
  8. [8]
    F. Kappel,The invariance of limit sets for autonomous functional differential equations, SIAM J. Appl. Math.,19 (1970), pp. 408–419.CrossRefzbMATHMathSciNetGoogle Scholar
  9. [9]
    R. K. Miller - G. R. Sell,Volterra integral equations and topological dynamics, Memoir of Amer. Math. Soc.,102, Providence, R. I. (1970).Google Scholar
  10. [10]
    M. A. Cruz -J. K. Hale,Stability of functional differential equations of neutral type, J. Diff. Equ.,7 (1970), pp. 334–355.CrossRefMathSciNetGoogle Scholar
  11. [11]
    J. K. Hale,Functional differential equations, Springer-Verlag, New York (1971).Google Scholar
  12. [12]
    M. R. Hildebrando,Invariança para sistemas autônomos de equaçoes differenciais com retardamento e applicaçoes, Master's Thesis, São Carlos (1970).Google Scholar
  13. [13]
    A. Strauss -J. A. Yorke,On asymptotically autonomous differential equations, Math. Systems Theor.,1 (1967), pp. 175–182.CrossRefMathSciNetGoogle Scholar
  14. [14]
    C. M. Dafermos,An invariance principle for compact processes, J. Diff. Equ.,9 (1971), pp. 239–252.CrossRefzbMATHMathSciNetGoogle Scholar
  15. [15]
    J. K. Hale -J. P. LaSalle -M. Slemrod,Theory of a general class of dissipative processes, J. Math. Analysis Appl.,39 (1972), pp. 177–191.CrossRefMathSciNetGoogle Scholar
  16. [16]
    N. Rouche,The invariance principle applied to non-compact limit sets, to appear in Boll. Un. Mat. Ital.Google Scholar
  17. [17]
    M. Fréchet,Les fonctions asymptotiquement presque périodiques, Rev. Sci.,79 (1941), pp. 341–357.zbMATHGoogle Scholar

Copyright information

© Fondazione Annali di Matematica Pura ed Applicata 1975

Authors and Affiliations

  • Nicolas Rouche
    • 1
  1. 1.Louvain-la-NeuveBelgium

Personalised recommendations