On the oscillation of solutions of a class of linear fourth order differential equations.

*(English)*Zbl 0547.34023Consider the equation (*) \(y^{(4)}+P(t)y''+R(t)y'+Q(t)y=0\), where P(t), R(t), and Q(t) are real-valued continuous functions on [a,\(\infty)\). The author shows the existence of monotonous solutions of (*) under the assumptions that P(t)\(\leq 0\), \(R^ 2(t)\leq 2P(t)Q(t)\) for all \(t\in [a,\infty)\), and Q(t) is not identically zero in any subinterval of [a,\(\infty)\). The author gives conditions for conjugation of equation (*) and necessary and sufficient conditions for (*) to be oscillatory and nonoscillatory respectively. The condition for oscillation is in terms of the behaviour of nonoscillatory solutions.

Reviewer: T.S.Liu

##### MSC:

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

34A30 | Linear ordinary differential equations and systems |

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##### References:

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