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.