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Oscillations of an equation relevant to an industrial problem

Published online by Cambridge University Press:  17 April 2009

Alexander Tomaras
Alexander Tomaras
Affiliation:
Mathematical Institute, University of Oxford, St Giles
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Abstract

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The oscillatory behaviour of the solutions of a functional differential equation, of more general form than an equation arising from in industrial problem, is examined. The question of whether one can maintain the oscillatory properties of this equation by adding a forcing term is also answered. The results obtained extend already known results on the subject and complete the relevant literature.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 12 , Issue 3 , June 1975 , pp. 425 - 431
Copyright
Copyright © Australian Mathematical Society 1975

References

[1]de Bruijn, N.G., “The difference-differential equation F′(x) = e αx + βF(x–1). I”, K. Nederl. Akad. Wetensch. Proc. Ser. A 56 = Indag. Math. 15 (1953), 449–458.CrossRefGoogle Scholar
[2]de Bruijn, N.G., “The difference-differential equation F′(x) = e αx+βF(x–1). II”, K. Nederl. Akad. Wetensch. Proc. Ser. A 56 = Indag. Math. 15 (1953), 459–464.CrossRefGoogle Scholar
[3]Dyson, Janet, “Some topics in functional differential equations”, (D. Phil. Thesis, Oxford, 1973).Google Scholar
[4]Fox, L., Mayers, D.P., Ockendon, J.R. and Tayler, A.B., “On a functional differential equation”, J. Inst. Math. Appl. 8 (1971), 271–307.CrossRefGoogle Scholar
[5]Kato, Tosio, “Asymptotic behaviour of solutions of the functional differential equation y′(x) = ay(λx) + by(x)”, Delay and functional differential equations and their applications, 197–217 (Proc. Conf. Park City, Utah, 1972. Academic Press, New York, London, 1972).CrossRefGoogle Scholar
[6]Kato, 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
[7]Kusano, T. and Onose, H., “Oscillations of functional differential equations with retarded argument”, J. Differential Equations 15 (1974), 269–277.CrossRefGoogle Scholar
[8]Ladas, G., Lakshmikantham, V. and Papadakis, J.S., “Oscillations of higher-order retarded differential equations generated by the retarded argument”, Delay and functional differential equations and their applications, 219–231 (Proc. Conf. Park City, Utah, 1972. Academic Press, New York, London, 1972).CrossRefGoogle Scholar
[9]Ockendon, J.R. and Tayler, A.B., “The dynamics of a current collection system for an electric locomotive”, Proc. Roy. Soc. London A 322 (1971), 447–468.Google Scholar