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Zbl 0860.34038
Grace, S.R.
Oscillation theorems of comparison type for neutral nonlinear functional differential equations.
(English)
[J] Czech. Math. J. 45, No.4, 609-626 (1995). ISSN 0011-4642; ISSN 1572-9141/e

The author considers the neutral differential equation $$(x(t)+ p(t)x(g_1(t)))^{(n)}+ q(t)f(x(g(t)))=0 \tag 1$$ and the forced neutral equation $$(x(t)+ p(t)x(g_1(t)))^{(n)}+ q(t)f(x(g(t)))= e(t), \tag 2$$ where $n$ is even, $p,q,g_1,g,e: [t_0,\infty)\to \bbfR$, $t_0>0$, $f:\bbfR\to \bbfR$ are continuous and $\lim_{t\to\infty} g_1(t)= \infty$, $\lim_{t\to\infty} g(t)= \infty$. \par It is proved that the equation (1) (or (2)) is oscillatory if some linear second order equation is oscillatory and moreover some other conditions hold. The equation (1) (or (2)) is oscillatory if all of their solutions are oscillatory.
[P.Marušiak (Žilina)]
MSC 2000:
*34K11 Oscillation theory of functional-differential equations
34K40 Neutral equations
34C10 Qualitative theory of oscillations of ODE: Zeros, etc.

Keywords: neutral differential equation; forced neutral equation; oscillatory

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