Neutral differential equations are studied. Sufficient conditions are obtained to have oscillatory solutions or nonoscillatory solutions. For the existence of solutions, the Schauder-Tikhonov fixed point theorem is used.

In this article, we obtain sufficient conditions so that every solution of neutral delay differential equation $${(y\left(t\right)-\sum _{i=1}^k{p}_i\left(t\right)y\left(r_i\left(t\right)\right))}^{\left(n\right)}+v\left(t\right)G\left(y\left(g\left(t\right)\right)\right)-u\left(t\right)H\left(y\left(h\left(t\right)\right)\right)=f\left(t\right)$$ oscillates or tends to zero as $t\to \infty$, where, $n\ge 1$ is any positive integer, $p_i$, $r_i\in C^{\left(n\right)}([0,\infty ),ℝ)$  and $p_i$ are bounded for each $i=1,2,\cdots ,k$. Further, $f\in C\left(\right[0,\infty ),ℝ)$, $g$, $h$, $v$, $u\in C\left(\right[0,\infty ),[0,\infty \left)\right)$, $G$ and $H\in C(ℝ,ℝ)$. The functional delays $r_i\left(t\right)\le t$, $g\left(t\right)\le t$ and $h\left(t\right)\le t$ and all of them approach $\infty$ as $t\to \infty$. The results hold when $u\equiv 0$ and $f\left(t\right)\equiv 0$. This article extends, generalizes and improves some recent results, and further answers some unanswered questions from the literature.

In this paper we are concerned with the oscillation of solutions of a certain more general higher order nonlinear neutral type functional differential equation with oscillating coefficients. We obtain two sufficient criteria for oscillatory behaviour of its solutions.

Sufficient conditions are obtained for oscillation of all solutions of a class of forced nth order linear and nonlinear neutral delay differential equations. Also, asymptotic behaviour of nonoscillatory solutions of a class of forced first order neutral equations is studied.

This paper deals with the second order nonlinear neutral differential inequalities $\left(A_{\nu }\right)$: ${(-1)}^{\nu }x\left(t\right)\{z^{\text{'}\text{'}}\left(t\right)+{(-1)}^{\nu }q\left(t\right)f\left(x\left(h\left(t\right)\right)\right)\}\le 0,$$t\ge t_0\ge 0...$

The purpose of this paper is to obtain oscillation criteria for the differential system $$\begin{array}{cc}\hfill {[y_1\left(t\right)-a\left(t\right)y_1\left(g\left(t\right)\right)]}^{\text{'}}& =p_1\left(t\right)f_1\left(y_2\left(h_2\left(t\right)\right)\right)\hfill \\ \hfill y_2^{\text{'}}\left(t\right)& =p_2\left(t\right)f_2\left(y_3\left(h_3\left(t\right)\right)\right)\hfill \\ \hfill y_3^{\text{'}}\left(t\right)& =-p_3\left(t\right)f_3\left(y_1\left(h_1\left(t\right)\right)\right),t\in {ℝ}_{+}=[0,\infty ).\hfill \end{array}$$