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Studies in multiplicative solutions to linear differential equations

Published online by Cambridge University Press:  14 November 2011

F. M. Arscott
F. M. Arscott
Affiliation:
Department of Applied Mathematics, University of Manitoba, Winnipeg, Manitoba, R3T 2N2, Canada
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Synopsis

Given an ordinary linear differential equation whose singularities are isolated, a solution is called multiplicative for a closed path C if, when continued analytically along C, it returns to its starting-point merely multiplied by a constant. This paper first classifies such paths into three types, then investigates combinations of two such paths, in which a number of qualitatively different situations can arise. A key result is also given relating to a three-path combination. There are applications to special functions and Floquet theory for periodic equations.

Information

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 106 , Issue 3-4 , 1987 , pp. 277 - 305
Copyright
Copyright © Royal Society of Edinburgh 1987

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References

1Arscott, F. M.. Periodic Differential Equations (Oxford: Pergamon, 1964).Google Scholar
2Arscott, F. M. and Sleeman, B. D.. Multiplicative solutions of linear differential equations. J. Lond. Math. Soc. (2) 43 (1968), 263–270.CrossRefGoogle Scholar
3, Erdélyi et al. (Bateman Manuscript Project). Higher Transcendental Functions, Vol. 1 (New York: McGraw-Hill, 1953).Google Scholar
4Ince, E. L.. Ordinary Differential Equations (London: Longmans – Dover, 1925).Google Scholar
5Magnus, W. and Winkler, S.. Hill's Equation (New York: Wiley, 1966).Google Scholar
6Sleeman, B. D., Smith, P. D. and Wright, G. P.. Doubly-periodic Floquet theory. Proc. Roy. Soc. London Ser. A 391 (1984) 125–147.Google Scholar