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Zbl 0829.34060
Li, Bingtuan
Oscillations of delay differential equations with variable coefficients.
(English)
[J] J. Math. Anal. Appl. 192, No.1, 312-321 (1995). ISSN 0022-247X

The author considers the equation in the form (1) $\dot x(t) + p(t) x(t - \tau) = 0$. The main result is one theorem: Let $p(t) \in C ([t_0, \infty), R_+)$, $\tau > 0$. Suppose that $\int^t_{t - \tau} p(s)ds \ge 1/e$ for $t \ge t_1 \ge t_0 + \tau$ and $\int^\infty_{t_0 + \tau} p(s) [\exp (\int^t_{t - \tau} p (s)ds - {1 \over e}) - 1] dt = \infty$. Then every solution of (1) oscillates.
[P.Marušiak (Žilina)]
MSC 2000:
*34K11 Oscillation theory of functional-differential equations
34C10 Qualitative theory of oscillations of ODE: Zeros, etc.

Keywords: linear delay differential equations; oscillatory solutions

Cited in: Zbl 0893.34065

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