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13.—The 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:
Mathematical Institute, Oxford.
Janet Dyson
Affiliation:
Mathematical Institute, Oxford.
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Synopsis

The paper discusses the asymptotic behaviour of solutions of the functional differential equation

where a is a complex constant, 0<λ<1, and b is a constant such that Re b = 0, but b ≠ 0.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 74 , 1976 , pp. 165 - 174
Copyright
Copyright © Royal Society of Edinburgh 1976

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References

1Carr, J. and Dyson, J.. The matrix functional differential equation y'(x) = Ay(λx)+By(x), to appear.Google Scholar
2Bruijn, N. G. De. The asymptotically periodic behaviour of the solutions of some linear functional equations. Amer. J. Math 71 (1949), 313–330.CrossRefGoogle Scholar
3Fox, 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
4Kato, 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
5Kato, 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— Proceedings of a conference, P. C. Utah 1972; Ed. Klaus Schmitt, .) (New York: Academic, 1972.)Google Scholar