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On oscillation and asymptotic property of a class of third-order differential equations. (English) Zbl 0955.34023

The authors study oscillatory, nonoscillatory and some other questions on the asymptotic behaviour of solutions to the equation \[ y'''+a(t)y''+b(t)y'+c(t)y=0, \tag \(*\) \] with \(a\in C^2([\sigma ,+\infty [;\mathbb{R})\), \(b\in C^{'}([\sigma ,+\infty [;\mathbb{R})\), \(c\in C([\sigma ,+\infty [;\mathbb{R})\) and \(a(t)\leq 0\), \(b(t)\geq 0\), \(c(t)< 0\) for \(t\geq \sigma \). In particular, they establish several effective conditions for the existence of oscillatory solutions to \((*)\) and conditions guaranteeing nonoscillation of all solutions to \((*)\).

MSC:

34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
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References:

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