MATHEMATICA BOHEMICA, Vol. 129, No. 1, pp. 11-27 (2004)

Oscillatory behaviour of solutions of nonlinear higher order neutral differential equations

N. Parhi, R. N. Rath

N. Parhi, Plot No. 1365/3110, Shastri Nagar, Unit-4, Bhubaneswar-751 001, Orissa, India, e-mail:; R. N. Rath, P. G. Department of Mathematics, Khallikote Autonomous College, Berhampur-760001, Orissa, India, e-mail:

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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