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Zbl 0996.34058
Zhang, Xiaosheng; Yan, Yurang
Oscillation criteria for first-order neutral differential equations with positive and negative coefficients.
(Chinese. English summary)
[J] Appl. Math., Ser. A (Chin. Ed.) 16, No.4, 401-406 (2001). ISSN 1000-4424

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 $P,Q,R\in C([t_0, \infty),\bbfR^+), r,\tau,\delta\in (0,\infty)$, $\tau\ge\delta$. 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 2000:
*34K11 Oscillation theory of functional-differential equations
34K40 Neutral equations

Keywords: oscillation; first-order neutral differential equations

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