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Nonoscillation of arbitrary order retarded differential equations of non-homogeneous type

Published online by Cambridge University Press:  17 April 2009

R.S. Dahiya
R.S. Dahiya
Affiliation:
Department of Mathematics, Iowa State University, Ames, Iowa, USA.
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The object of the present paper is to study the delay differential equation of arbitrary order namely y(n)(t) + a(t)yτ(t) = f(t), n≥2 (an integer) and prove a nonoscillation theorem under the general situation in which a(t) and f(t) are allowed to oscillate arbitrarily often on some positive half real line. This is accomplished by way of two differential inequalities of nth order.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 10 , Issue 3 , June 1974 , pp. 453 - 458
Copyright
Copyright © Australian Mathematical Society 1974

References

[1]Dahiya, R.S. and Singh, B., “On oscillatory behavior of even order delay equations”, J. Math. Anal. Appl. 42 (1973), 183–189.Google Scholar
[2]Onose, Hiroshi, “Oscillatory property of ordinary differential equations of arbitrary order”, J. Differential Equations 7 (1970), 454–458.Google Scholar
[3]Singh, B., “Oscillation and nonoscillation of even order nonlinear delay differential equations”, Quart. Appl. Math. (to appear).Google Scholar
[4]Singh, Bhagat and Dahiya, R.S., “Nonoscillation of third order retarded equations”, Bull. Austral. Math. Soc. 10 (1974), 9–14.Google Scholar