Oscillation criteria for first-order neutral differential equations with positive and negative coefficients. (Chinese. English summary) Zbl 0996.34058

Zhang, Xiaosheng; Yan, Yurang

Appl. Math., Ser. A (Chin. Ed.) 16, No. 4, 401-406 (2001).

Summary: Consider the neutral equation \[ {d\over dt}\bigl[x(t)-R(t)x(t-r) \bigr]+P(t)x (t-\tau)-Q(t)x(t- \delta)=0 \tag{*} \] with \(P,Q,R\in C([t_0, \infty),\mathbb{R}^+), r,\tau,\delta\in (0,\infty)\), \(\tau\geq\delta\). Oscillating criteria for equation (*) are obtained in the case where \(R(t)+ \int^t_{t-\tau +\delta} Q(u)du-1\) is allowed to change its sign.

MSC:

34K11	Oscillation theory of functional-differential equations
34K40	Neutral functional-differential equations

Keywords:

oscillation; first-order neutral differential equations