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**Nonoscillation and asymptotic behaviour for third order nonlinear differential equations.**
*(English)*
Zbl 0955.34025

Summary: The authors consider the equation
\[
y''' + q(t)y'{}^{\alpha }+p(t)h(y) =0,
\]
where \(p,q\) are real-valued continuous functions on \([0,\infty)\) such that \(q(t) \geq 0\), \(p(t) \geq 0\) and \(h(y)\) is continuous in \((-\infty ,\infty)\) such that \(h(y)y>0\) for \(y\not = 0\). They obtain sufficient conditions for solutions to the considered equation to be nonoscillatory. Furthermore, the asymptotic behaviour of these nonoscillatory solutions is studied.

### MSC:

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

34D05 | Asymptotic properties of solutions to ordinary differential equations |

### Keywords:

third-order nonlinear differential equations; nonoscillatory solutions; asymptotic properties of solutions
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\textit{A. Tiryaki} and \textit{A. O. Çelebi}, Czech. Math. J. 48, No. 4, 677--685 (1998; Zbl 0955.34025)

### References:

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