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2.—The Matrix Functional Differential Equation y′(x) = Ay(λx) + By(x)*

Published online by Cambridge University Press:  14 February 2012

Jack Carr  and
Janet Dyson
Jack Carr
Affiliation:
Department of Mathematics, Heriot-Watt University, Edinburgh
Janet Dyson
Affiliation:
Mathematical Institute, Oxford.
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Synopsis

The purpose of this work is to consider some analytic aspects of the matrix functional differential equation, y′(x) = Ay(λx) + By(x), (0 ≦ x < ∞), where λ is a constant with 0 < λ < 1 and A and B are constant matrices.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 75 , Issue 1 , 1976 , pp. 5 - 22
Copyright
Copyright © Royal Society of Edinburgh 1976

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References

1de Bruijn, N. G.. The difference-differential equation F′(x) = e axa + βF(x−l). I. Nederl. Akad Wetensch. Proc. Ser. A 56 (1953), 449–458. II. Indag. Math. 15 (1953), 359–464.CrossRefGoogle Scholar
2Carr, Jack. The asymptotic behaviour of the solutions of some linear funtional differential equations (Oxford Univ. D.Phil. Thesis, 1974).Google Scholar
3Dyson, Janet. Some topics in functional differential equations (Oxford Univ. D.Phil Thesis, 1973).Google Scholar
4Fox, L., Mayers, D. F., Ockendon, J. R. and Tayler, A. B.. On a functional differential equation. J. Inst. Math. Appl. 8 (1971), 271–307.CrossRefGoogle Scholar
5Kato, Tosio and McLeod, J. B.. The functional differential equation y′(x) = ay(λx)+by(x). Bull. Amer. Math. Soc. 77 (1971), 891–937.Google Scholar
6Kato, Tosio. Asymptotic behaviour of solutions of the functional differential equation y′(x) = ay(λx)+by(x). In Delay and functional differential equations and their applications (Ed. Klaus, Schmitt) (New York: Academic Press, 1972).Google Scholar
7Ockendon, J. R. and Tayler, A. B.. The dynamics of a current collection system for a an electric locomotive. Proc. Roy. Soc. London Ser. A 322 (1971), 447–468.Google Scholar