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Zbl 1005.34056
Shen, J.H.; Debnath, L.
Oscillations of solutions of neutral differential equations with positive and negative coefficients. (English)
[J] Appl. Math. Lett. 14, No.6, 775-781 (2001). ISSN 0893-9659

The authors consider the neutral differential equation with positive and negative coefficients of the form $$ \frac{d}{dt}[y(t)-R(t)y(t-r)]+P(t)y(t-\tau)-Q(t)y(t-\sigma)=0, $$ where $r\in (0, \infty)$, and $\tau , \sigma \in \bbfR^+$ with $\tau \ge\sigma $; $P, Q, R\in C([t_0, \infty), \bbfR^+), P(t)-Q(t-\tau+\sigma)\ge 0$ and not identically zero. Several new sufficient conditions for the oscillation of all solutions to the above equation are obtained without the following usual hypothesis: $\int_{t_0}^{\infty}[P(s)-Q(s-\tau+\sigma)] ds=\infty$.
[Qiru Wang (Guangzhou)]

MSC 2000:: *34K11 Oscillation theory of functional-differential equations
34K40 Neutral equations

Keywords: neutral differential equations; oscillation

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