# zbMATH — the first resource for mathematics

Oscillation of higher order nonlinear neutral functional differential equation. (English) Zbl 0849.34059
The paper deals with the neutral functional differential equation (1) $$[x(t) - P(t) x(t - \tau)]^{(n)} + Q(t) f (x (t - \sigma)) = 0$$ where $$n \geq 1$$ is odd, $$\tau$$ and $$\sigma$$ are positive constants, $$P,Q \in C ([t_0, + \infty), \mathbb{R}^+)$$, $$f\in C(\mathbb{R},\mathbb{R})$$, $$f$$ is nondecreasing, $$xf(x) > 0$$ for $$x \neq 0$$. The author presents sufficient conditions for either all solutions of (1) to be oscillatory or all bounded solutions of (1) to be oscillary.

##### MSC:
 34K11 Oscillation theory of functional-differential equations 34K40 Neutral functional-differential equations 34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations