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

The purpose of this paper is to obtain oscillation criterions for the differential system of neutral type.

We consider first order neutral functional differential equations with multiple deviating arguments of the form ${(x\left(t\right)+Bx(t-\delta ))}^{\text{'}}=g₀(t,x\left(t\right))+{\sum }_{k=1}^n{g}_k(t,x(t-{\tau }_k\left(t\right)))+p\left(t\right)$. By using coincidence degree theory, we establish some sufficient conditions on the existence and uniqueness of periodic solutions for the above equation. Moreover, two examples are given to illustrate the effectiveness of our results.

By using the coincidence degree theory, we study a type of $p$-Laplacian neutral Rayleigh functional differential equation with deviating argument to establish new results on the existence of $T$-periodic solutions.

This paper deals with the existence of positive $\omega$-periodic solutions for the neutral functional differential equation with multiple delays $${(u\left(t\right)-cu(t-\delta ))}^{\text{'}}+a\left(t\right)u\left(t\right)=f(t,u(t-{\tau }_1),\cdots ,u(t-{\tau }_n)).$$ The essential inequality conditions on the existence of positive periodic solutions are obtained. These inequality conditions concern with the relations of $c$ and the coefficient function $a\left(t\right)$, and the nonlinearity $f(t,x_1,\cdots ,x_n)$. Our discussion is based on the perturbation method of positive operator and fixed point index theory in cones.