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Nonoscillation of third order retarded equations

Published online by Cambridge University Press:  17 April 2009

Bhagat Singh  and
R.S. Dahiya
Bhagat Singh
Affiliation:
Department of Mathematics, University of Wisconsin, Manitowoc Center, Mani towoc, Wisconsin, USA;
R.S. Dahiya
Affiliation:
Department of Mathematics, Iowa State University, Ames, Iowa, USA.
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The third order delay equation

y‴(t) + a(t)yτ(t) = 0

is studied for its nonoscillatory nature under the general condition in which a(t) has been allowed to oscillate. It is shown by way of a differential inequality that if g(t) is a thrice differentiable and eventually positive function then

g‴(t) + t2|a(t)|g(t) ≤ 0

is sufficient for this equation to have bounded nonoscillatory solutions.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 10 , Issue 1 , February 1974 , pp. 9 - 14
Copyright
Copyright © Australian Mathematical Society 1974

References

[1]Keener, Marvin S., “On the solutions of certain linear nonhomogeneous second-order differential equations”, Applicable Anal. 1 (1971), 57–63.CrossRefGoogle Scholar
[2]Onose, Hiroshi, “Oscillatory property of ordinary differential equations of arbitrary order”, J. Differential Equations 7 (1970), 454–458.CrossRefGoogle Scholar
[3]Singh, Bhagat, “A necessary and sufficient condition for the oscillation of even order nonlinear delar differential equation”, Canad. J. Math. (to appear).Google Scholar
[4]Wong, James S.W., “Second order oscillation with retarded arguments”, Ordinary differential equations, 1971 NRL-MRC Conference, 581–596 (Academic Press, New York and London, 1972).Google Scholar