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Necessary and sufficient condition for oscillations of neutral differential equations

Published online by Cambridge University Press:  17 February 2009

M. R. S. Kulenović ,
G. Ladas  and
A. Meimaridou
M. R. S. Kulenović
Affiliation:
Department of Mathematics, University of Rhode Island, Kingston, R.I. 02881, USA. Department of Mathematics, University of Sarajevo, Sarajevo 71000, Yugoslavia.
G. Ladas
Affiliation:
Department of Mathematics, University of Rhode Island, Kingston, R.I. 02881, USA.
A. Meimaridou
Affiliation:
Department of Mathematics, University of Rhode Island, Kingston, R.I. 02881, USA. Department of Electrical Engineering, Democritus University of Thrace, Xanthi 67100, Greece.
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Abstract

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Consider the neutral delay differential equation

where p ∈ R, τ ≥ 0, q1 > 0, σ1 ≥ 0, for i = 1, 2, …, k. We prove the following result.

Theorem. A necessary and sufficient condition for the oscillation of all solutions of Eq. (1) is that the characteristic equation

has no real roots.

Type
Research Article
Information
The ANZIAM Journal , Volume 28 , Issue 3 , January 1987 , pp. 362 - 375
Copyright
Copyright © Australian Mathematical Society 1987

References

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