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On the stability and boundedness of differential systems in Banach spaces

Published online by Cambridge University Press:  24 October 2008

Chris P. Tsokos
Affiliation:
University of Rhode Island, Kingston, R.I.
M. Rama Mohana Rao
Affiliation:
University of Rhode Island, Kingston, R.I.

Extract

In this paper we are investigating boundedness and certain stability properties of differential systems in spaces, utilizing the generalization of Bellman's Lemma which was formulated by one of the authors (8).

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1969

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References

REFERENCES

(1)Kamke, E.Differentialgleichungen reeller Funktionen. Akademische Verlagsgesellschaft (Leipzig, 1930).Google Scholar
(2)Kato, T.Integration of the equation of evolution in a Banach space. J. Math. Soc. Japan 5 (1953), 208304.Google Scholar
(3)Kato, T.On linear differential equations in Banach space. Comm. Pure Appl. Math. 9 (1956), 479486.CrossRefGoogle Scholar
(4)Krasnoselskii, M. A., Krein, S. G. and Soboleveskii, P. E.On differential equations with unbounded operators in Banach spaces. Dokl. Akad. Nauk. SSSR 111 (1956), 1922.Google Scholar
(5)Krasnoselskii, M. A., Krein, S. G. and Soboleveskii, P. E.On differential equations with unbounded operators in Banach spaces. Dokl. Akad. Nauk. SSSR 112 (1957), 990993.Google Scholar
(6)Lakshmikantham, V.On the stability and boundedness of differential systems. Proc. Cambridge Philos. Soc. 58 (1962), 492496.CrossRefGoogle Scholar
(7)Mlak, W.Limitations and dependence on parameters of solutions of non-stationary differential operator equations. Ann. Polon. Math. 6 (1959), 305322.CrossRefGoogle Scholar
(8)Rama Mohana Rao, M.A note on an integral inequality. J. Indian Math. Soc. 27 (1963), 6769.Google Scholar
(9)Yoshizawa, T.Lyapunov's function and boundedness of solutions. Funkcial. Ekvac. 2 (1959), 95142.Google Scholar
(10)Yoshizawa, T.Stability and boundedness of systems. Arch. Rational Mech. Anal. 6 (1960), 409421.CrossRefGoogle Scholar