Hostname: page-component-586b7cd67f-gb8f7 Total loading time: 0 Render date: 2024-11-28T15:08:10.018Z Has data issue: false hasContentIssue false

Oscillatory behaviour of first order delay differential equations

Published online by Cambridge University Press:  17 April 2009

Alexander Tomaras
Affiliation:
Mathematical Institute, University of Oxford, Oxford, England.
Rights & Permissions [Opens in a new window]

Abstract

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.

Best possible conditions are given here, under which all solutions of several delay differential equations are oscillatory.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1979

References

[1]Cooke, Kenneth L. and Yorke, James A., “Equations modelling population growth, economic growth, and gonorrhea epidemiology”, Ordinary differential equations, 1971 NRL–MRC Conference, 3553 (Proc. Conf. Ordinary Differential Equations held Washington, D.C., 1971. Academic Press, New York and London, 1972).Google Scholar
[2]Driver, R.D., “Linear differential systems with small delays”, J. Differential Equations 21 (1976), 148166.CrossRefGoogle Scholar
[3]Fox, L., Mayers, D.F., Ockendon, J.R. and Tayler, A.B., “On a functional differential equation”, J. Inst. Math. Appl. 8 (1971), 271307.CrossRefGoogle Scholar
[4]Kato, Tosio, “Asymptotic behaviour of solutions of the functional differential equation y′(x) = ayx) + by(x)”, Delay and functional differential equations and their applications, 197217 (Proc. Conf. Park City, Utah, 1972. Academic Press, New York, London, 1972).CrossRefGoogle Scholar
[5]Kato, Tosio and McLeod, J.B., “The functional-differential equation y′(x) = ayx) + by(x)”, Bull. Amer. Math. Soc. 77 (1971), 891937.Google Scholar
[6]Ladas, Gerasimos, “Sharp conditions for oscillations caused by delays” (Technical Report, 64. Department of Mathematics, University of Rhode Island, Kingston, Rhode Island, 1976).Google Scholar
[7]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, 219231 (Proc. Conf. Park City, Utah, 1972. Academic Press, New York, London, 1972).CrossRefGoogle Scholar
[8]Lillo, James C., “Oscillatory solutions of the equation y′(x) = m(x)y(xn(x))”, J. Differential Equations 6 (1969), 135.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), 447468.Google Scholar
[10]Tomaras, Alexander, “Oscillations of an equation relevant to an industrial problem”, Bull. Austral. Math. Soc. 12 (1975), 425431.CrossRefGoogle Scholar
[11]Tomaras, Alexander, “Oscillatory behaviour of an equation arising from an industrial problem”, Bull. Austral. Math. Soc. 13 (1975), 255260.CrossRefGoogle Scholar
[12]Yorke, James A., “Selected topics in differential delay equations”, Japan-United States Seminar on Ordinary Differential and Functional Equations, 1628 (Lecture Notes in Mathematics, 243. Springer-Verlag, Berlin, Heidelberg, New York, 1971).CrossRefGoogle Scholar