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MATHEMATICA BOHEMICA, Vol. 129, No. 1, pp. 11-27 (2004)
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Oscillatory behaviour of solutions of nonlinear higher order neutral differential equations

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N. Parhi, R. N. Rath

* N. Parhi*, Plot No. 1365/3110, Shastri Nagar, Unit-4, Bhubaneswar-751 001, Orissa, India, e-mail: ` parhi2002@rediffmail.com`; * R. N. Rath*, P. G. Department of Mathematics, Khallikote Autonomous College, Berhampur-760001, Orissa, India, e-mail: ` radhanathmath@yahoo.co.in`

**Abstract:** Necessary and sufficient conditions are obtained for oscillation of all bounded solutions of

[y(t) - y(t-\tau )]^{(n)} + Q(t) G(y(t-\sigma )) = 0, t \ge 0, \tag $*$

where $n \ge 3$ is odd. Sufficient conditions are obtained for all solutions of $(*)$ to oscillate. Further, sufficient conditions are given for all solutions of the forced equation associated with $(*)$ to oscillate or tend to zero as $t \rightarrow \infty $. In this case, there is no restriction on $n$.

**Keywords:** oscillation, nonoscillation, neutral differential equations

**Classification (MSC2000):** 34C10, 34C15, 34K40

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