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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 \(p(t) \leq 0\), \(q(t) > 0\) or \(p(t) \leq 0\), \(p'(t) - q(t) > 0\) 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:
34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
34A30 Linear ordinary differential equations and systems
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