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Oscillation of solutions of non-linear neutral delay differential
equations of higher order for $p(t) = \pm 1$

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*R. N. Rath,
L. N. Padhy, N. Misra*

**Address.**

R. N. Rath, P. G. Department of Mathematics, Khallikote College,
Berhampur 760001, Orissa, India

L. N. Padhy,
Department of Mathematics,
Konark Institute of Science and Technology,
Jatni--752050, Bhubaneswar,
Orissa, India

N. Misra, P. G. Department of Mathematics, Berhampur University, Berhampur 760007,
Orissa, India

**E-mail. **rathanathmath@yahoo.co.in

**Abstract.**

In this paper, the oscillation criteria for solutions of
the neutral delay differential equation (NDDE)
\[
\left( {y(t)-p(t)\,
y({t-\tau} )}
\right)^{(n )}+
\alpha \,Q(t)\,\,G\left( {y({t-\sigma })} \right)=
f(t)
\]
has been studied where $p(t) = 1$ or $p(t) \le 0$,
$\alpha =\pm 1$, $Q\in C \left([0, \infty ), R^{+}\right)$, $f \in
C([0, \infty ), R)$, $G \in
C(R, R)$. This work improves and generalizes some recent
results and answer
some questions that are raised in [1].

**AMSclassification. **34C10, 34C15, 34K40.

**Keywords. ** Oscillation, non-oscillation, neutral equations,
asymptotic-behaviour.