**Oscillatory and asymptotic behaviour of a neutral differential equation with oscillating coefficients**

**J. G. Dix**, Texas State University, San Marcos, Texas, U. S. A **N. Misra**, Berhampur University, Berhampur, Orissa, India**L. N. Padhy**, K.I.S.T., Bhubaneswar, Orissa, India**R. N. Rath**, Khallikote Autonomous College, Berhampur, Orissa, India

E. J. Qualitative Theory of Diff. Equ., No. 19. (2008), pp. 1-10.

Communicated by P. Eloe.
| Received on 2008-02-11 Appeared on 2008-05-15 |

**Abstract: **In this paper, we obtain sufficient conditions so that every solution of

$$

\big(y(t)- \sum_{i=1}^n p_i(t) y(\delta_i(t))\big)'+\sum_{i=1}^m q_i(t) y(\sigma_i(t)) = f(t)

$$

oscillates or tends to zero as $t \to \infty$. Here the coefficients $p_i(t), q_i(t)$ and the forcing term $f(t)$ are allowed to oscillate; such oscillation condition in all coefficients is very rare in the literature. Furthermore, this paper provides an answer to the open problem 2.8.3 in [7, p. 57]. Suitable examples are included to illustrate our results.

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