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On some integrodifferential equations in Banach spaces

Published online by Cambridge University Press:  17 April 2009

B.G. Pachpatte
B.G. Pachpatte
Affiliation:
Department of Mathematics, Deogiri College Aurangabad, Maharashtra, India.
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Abstract

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This paper is concerned with the stability, boundedness, and asymptotic behavior of solutions of integrodifferential systems of the form

We shall also investigate the behavioral relationships between the solutions of two integrodifferential systems related to this system.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 12 , Issue 3 , June 1975 , pp. 337 - 350
Copyright
Copyright © Australian Mathematical Society 1975

References

[1]Friedman, Avner and Shinbrot, Marvin, “Volterra integral equations in Banach space”, Trans. Amer. Math. Soc. 126 (1967), 131–179.CrossRefGoogle Scholar
[2]Lakshmikantham, V., “Differential equations in Banach spaces and the extension of Lyapunov's method”, Proc. Cambridge Philos. Soc. 59 (1963), 373–381.CrossRefGoogle Scholar
[3]Lakshmikantham, V. and Leela, S., Differential and integral inequalities: theory and applications. Volume I: Ordinary differential equations (Mathematics in Science and Engineering, 55–1. Academic Press, New York and London, 1969).Google Scholar
[4]Lakshmikantham, V. and Leela, S., Differential and integral inequalities: theory and applications. Volume II: Functional, partial, abstract, and complex differential equations (Mathematics in Science and Engineering, 557–II. Academic Press, New York and London, 1969).Google Scholar
[5]Lovelady, David Lowell, “A functional differential equation in a Banach space”, Funkcial. Ekvac. 14 (1971), 111–122.Google Scholar
[6]Lovelady, David Lowell, “A global existence theorem for a functional differential equation”, An. Sti. Univ. “Al. I. Cuza” Iasi Sect. I a Mat. 18 (1972), 343–349Google Scholar
[7]Marti, Jürg T., “On integro-differential equations in Banach spaces”, Pacific J. Math. 20 (1967), 99–108.CrossRefGoogle Scholar
[8]Nohel, J.A., “Some problems in nonlinear Volterra integral equations”, Bull. Amer. Math. Soc. 68 (1962), 323–329.CrossRefGoogle Scholar
[9]Pachpatte, B.G., “Comparison theorems for integro-differential equations in Banach spaces”, Proc. Nat. Acad. Sci. India 42(A) (1972), 125–128.Google Scholar
[10]Pachpatte, B.G., “A note on Gronwall-Bellman inequality”, J. Math. Anal. Appl. 44 (1973), 758–762.CrossRefGoogle Scholar
[11]Pachpatte, B.G., “On the stability and asymptotic behavior of solutions of integrodifferential equations in Banach spaces”, J. Math. Anal. Appl. (to appear).Google Scholar