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Integral criteria of oscillation for a third order linear differential equation. (English) Zbl 0855.34038
The differential equation (1) $y''' + p(t)y' + q(t)y = 0$ is considered, where either $p(t) \le 0$, $q(t) > 0$ or $p(t) \le 0$, $p'(t) - q(t) > 0$ on $I = (a, \infty) \subset (0, \infty)$. New criteria for (1) to be oscillatory on $I$ (i.e. (1) has at least one oscillatory solution on $I)$ are presented in integral form. These criteria extend and improve some oscillation ones for (1) and may be applied to the Euler equation.

MSC:
34C10Qualitative theory of oscillations of ODE: zeros, disconjugacy and comparison theory
34A30Linear ODE and systems, general
WorldCat.org
Full Text: EuDML
References:
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