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Global results and stability of motion†

Published online by Cambridge University Press:  24 October 2008

V. Lakshmikantham  and
S. Leela
V. Lakshmikantham
Affiliation:
University of Rhode Island and State University College of New York
S. Leela
Affiliation:
University of Rhode Island and State University College of New York
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Extract

1. The proofs of many results in the theory of stability and boundedness basically depend on dividing the vicinity of some kind of invariant set (or other convenient set) into suitable subsets and then trying either to prove that solutions cannot leave such sets or to estimate the escape time. This observation makes it possible to give some global results in terms of arbitrary sets which can be employed as tools in dealing with various problems of stability and boundedness. In applications, these tools enlarge the class of useful Lyapunov like functions and also offer more flexibility.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 70 , Issue 1 , July 1971 , pp. 95 - 102
Copyright
Copyright © Cambridge Philosophical Society 1971

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References

REFERENCES

(1)Lakshmikantham, V. and Leela, S.Differential and integral inequalities, theory and applications, Vol. I (New York, Academic Press, 1969).Google Scholar
(2)Rouche, N. and Dang-Chau, Phien. Sufficient stability conditions based on global lemmas; to appear in the Proc. International Symp. Nonlinear oscillations, Kiev, U.S.S.R. (1969).Google Scholar
(3)Leela, S. Lyapunov stability and conditional invariant sets. To appear.Google Scholar