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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
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References:

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