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On Infinite Systems of Linear Differential Equations

Published online by Cambridge University Press:  20 November 2018

J. P. McClure  and
R. Wong
J. P. McClure
Affiliation:
University of Manitoba, Winnipeg, Manitoba
R. Wong
Affiliation:
University of Manitoba, Winnipeg, Manitoba
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Let A = [αtj] (i,j = 1, 2, …) be an infinite matrix with complex entries, and let z = (ζj) (j = 1, 2, …) be a sequence of complex numbers. In this paper we wish to investigate the existence, uniqueness and asymptotic behavior of solutions to the infinite system of linear differential equations

with the initial conditions

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 27 , Issue 3 , 01 June 1975 , pp. 691 - 703
Copyright
Copyright © Canadian Mathematical Society 1975

References

1. Arley, N. and Borchsenius, V., On the theory of infinite systems of differential equations and their application to the theory of stochastic processes and the perturbation theory of quantum mechanics, Acta Math. 6 (1945), 261–322.Google Scholar
2. Bellman, R., The boundedness of solutions of infinite systems of linear differential equations, Duke Math. J. H (1947), 695–706.Google Scholar
3. Hille, E., Pathology of infinite systems of linear first order differential equations with constant coefficients, Ann. Mat. Pura Appl. 55 (1961), 133–148.Google Scholar
4. Hille, E. and Phillips, R. S., Functional analysis and semi-groups, Amer. Math. Soc. Colloq. Publ., vol. 81 (Amer. Math. Soc, Providence, R.I., 1957).Google Scholar
5. Charles Kahane, Stability of solutions of linear systems with dominant main diagonal, Proc. Amer. Math. Soc. 33 (1972), 69–71.Google Scholar
6. Krein, S. G., Linear differential equations in Banach space, Translations of Mathematical Monographs, vol. 29 (Amer. Math. Soc, Providence, R.I., 1971).Google Scholar
7. Lakshmikantham, V. and Leela, S., Differential and integral inequalities, vol. 1 (Academic Press, New York, 1969).Google Scholar
8. Oguzt, M. N.ôreli, On an infinite system of differential equations occurring in the degradations of polymers, Utilitas Math. 1 (1972), 141–155.Google Scholar
9. Shaw, Leonard, Existence and approximation of solutions to an infinite set of linear timeinvariant differential equations, SIAM J. Appl. Math. 22 (1972), 266–279.Google Scholar