Oscillation of higher order nonlinear neutral functional differential equation. (English) Zbl 0849.34059

Tang, Dequan

Ann. Differ. Equations 12, No. 1, 83-88 (1996).

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.

Reviewer: J.Ohriska (Košice)

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

Keywords:

neutral functional differential equation; bounded solutions; oscillary