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Annali di Matematica Pura ed Applicata

, Volume 92, Issue 1, pp 85–93 | Cite as

Asymptotically self invariant sets and perturbed systems

  • S. Leela
Article

Summary

Necessary conditions are obtained for the asymptotically self-invariant sets to be uniformly stable in variation and uniformly asymptotically stable in variation and hese results are employed to study the effect of certain perturbations on asymptotically self-invariant sets.

Keywords

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References

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    F. Brauer -A. Strauss,Perturbations of nonlinear systems of differential equations, III, J. Math. Anal. Appl.,31 (1970), pp. 37–48.CrossRefMathSciNetGoogle Scholar
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    F. Brauer,Perturbations of nonlinear systems, IV, MRC. Tech. Summary Report no. 1070 (1970).Google Scholar
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    W. A. Coppel,Stability and asymptotic behavior of differential equations, Heath, Boston, 1965.Google Scholar
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    V. Lakshmikantham -S. Leela,Differential and integral inequalities, Vols. I and II, Academic Press, New York, 1969.Google Scholar
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    V. Lakshmikantham -S. Leela,Asymptotically self-invariant sets and conditional stability, Proc. Intern. Symp. Diff. Eqns. and Dyn. Systems, Puerto Rico, 1965; Academic Press, New York, 1967, pp. 363–373.Google Scholar
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    T. Yoshizawa,The stability theory by Lyapunov's second method, Math. Soc. Japan, Tokyo, 1967.Google Scholar

Copyright information

© Nicola Zanichelli Editore 1972

Authors and Affiliations

  • S. Leela
    • 1
  1. 1.New YorkU.S.A

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