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 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 $$\begin{array}{cc}\hfill {[y_1\left(t\right)-a\left(t\right)y_1\left(g\left(t\right)\right)]}^{\text{'}}& =p_1\left(t\right)f_1\left(y_2\left(h_2\left(t\right)\right)\right)\hfill \\ \hfill y_2^{\text{'}}\left(t\right)& =p_2\left(t\right)f_2\left(y_3\left(h_3\left(t\right)\right)\right)\hfill \\ \hfill y_3^{\text{'}}\left(t\right)& =-p_3\left(t\right)f_3\left(y_1\left(h_1\left(t\right)\right)\right),t\in {ℝ}_{+}=[0,\infty ).\hfill \end{array}$$

We study solutions tending to nonzero constants for the third order differential equation with the damping term $${\left(a_1\left(t\right){\left(a_2\left(t\right)x^{\text{'}}\left(t\right)\right)}^{\text{'}}\right)}^{\text{'}}+q\left(t\right)x^{\text{'}}\left(t\right)+r\left(t\right)f\left(x\left(\varphi \left(t\right)\right)\right)=0$$ in the case when the corresponding second order differential equation is oscillatory.

The aim of this paper is to present sufficient conditions for all bounded solutions of the second order neutral differential equations of the form (r(t)(x(t) - px(t-τ))')' - q(t)f(x(σ(t))) = 0 to be oscillatory and to compare some existing results.

Some Wintner and Nehari type oscillation criteria are established for the second-order linear delay differential equation.

We study oscillatory properties of solutions of the system of differential equations of neutral type.

Effective sufficient conditions for oscillation and nonoscillation of solutions of some operator-differential equations with piecewise constant argument are found.