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