Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2024-12-27T01:56:49.808Z Has data issue: false hasContentIssue false

Infinite Systems of Differential Equations

Published online by Cambridge University Press:  20 November 2018

J. P. McClure
Affiliation:
University of Manitoba, Winnipeg, Manitoba
R. Wong
Affiliation:
University of Manitoba, Winnipeg, Manitoba
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In an earlier paper [7], we have studied the existence, uniqueness and asymptotic behavior of solutions to certain infinite systems of linear differential equations with constant coefficients. In the present paper we are interested in systems of nonlinear equations whose coefficients are not necessarily constants; more specifically, we are concerned with infinite systems of the form

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1976

References

1. Bellman, R., Tlte boundedness of solutions of infinite systems of linear differential equations, Duke Math. J. U (1947), 695706.Google Scholar
2. Coppel, W. A., Stability and asymptotic behavior of differential equations (Heath Math. Monographs, Boston, 1965).Google Scholar
3. Edwards, R. E., Functional analysis theory and applications (Holt, Rinehart, Winston, New York etc., 1965).Google Scholar
4. Fink, A. M., Almost periodic solutions to forced Lienard equations, Proc. 6th International Conference on Nonlinear Oscillations, 1974, pp. 95105.Google Scholar
5. Kahane, Charles, Stability of solutions of linear systems with dominant main diagonal, Proc. Amer. Math. Soc. 33 (1972), 6971.Google Scholar
6. Lakshmikantham, V. and Leela, S., Differential and integral inequalities, vol. 1 (Academic Press, New York, 1969).Google Scholar
7. McClure, J. P. and Wong, R., On infinite systems of linear differential equations, Can. J. Math. 27 (1975), 691703.Google Scholar
8. Shaw, Leonard, Solutions for infinite-matrix differential equations, J. Math. Anal. Appl. If.1 (1973), 373383.Google Scholar