On nonoscillatory solutions of a class of nonlinear differential equations.

*(English)*Zbl 0604.34020Let the quasi-derivatives of y be defined by \(L_ 0y=a_ 0(t)y\), \(L_ iy=a_ i(t)(L_{i-1}y)'\), \(a_ i\), \(i=1,...,n\) are positive continuous functions on [a,\(\infty)\) such that \(\int^{\infty}_{a}a_ i^{- 1}(t)dt=\infty.\) The equation \(L_ ny+(-1)^ nf(t,y,y',...,y^{(m)})=0,\) \(m\in \{0,1,...,n-1\}\) and \(L_ ny\) is the quasi-derivative of y of order n is studied. It is established that every nonoscillatory solution of the problem belongs to a set defined before. Existence was studied in a previously published work.

Reviewer: W.Ames

##### MSC:

34C15 | Nonlinear oscillations and coupled oscillators for ordinary differential equations |

34A34 | Nonlinear ordinary differential equations and systems |

34A99 | General theory for ordinary differential equations |

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\textit{J. Mikunda} and \textit{J. Rovder}, Math. Slovaca 36, 29--38 (1986; Zbl 0604.34020)

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##### References:

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[2] | LOVELADY D. L.: On the oscillatory behaviour of bounded solutions of higher order differential equations. J. Differential Equations 19, 1975, 167-175. · Zbl 0333.34030 |

[3] | ROVDER J.: Nonoscillatory solutions of n-th order nonlinear differential equation. Čas. pro pěst. mat. 107, 1982, 159-166. · Zbl 0501.34033 |

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