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On the stability of a second-order differential equation

Published online by Cambridge University Press:  09 April 2009

D. E. Daykin  and
K. W. Chang
D. E. Daykin
Affiliation:
University of Malaya, Kuala Lumpur.
K. W. Chang
Affiliation:
University of Malaya, Kuala Lumpur.
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In this note we discuss the stability at the origin of the solutions of the differential equation where a dot indicates a differentiation with respect to time, and α, β are real-valued functions of any arguments. We tacitly assume that α, β are such that solutions to (1) do in fact exist. Under the transformation equation (1) takes the equivalent familiar form .

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 5 , Issue 1 , February 1965 , pp. 8 - 16
Copyright
Copyright © Australian Mathematical Society 1965

References

[1]Rosenbrock, H. H., On the Stability of A Second-Order Differential Equation, J. London Math. Soc. 39 (1964), 77–80.CrossRefGoogle Scholar
[2]La Salle, J. and Lefschetz, S., Stability by Liapunov's Direct Method with Applications, Academic Press, New York (1961).Google Scholar