Czechoslovak Mathematical Journal, Vol. 48, No. 4, pp. 677-685, 1998

Nonoscillation and asymptotic behaviour for third order nonlinear differential equations

Aydin Tiryaki, A. Okay Celebi

Aydin Tiryaki, Hacettepe University, Faculty of Science, Mathematics Department, 06532 Beytepe-Ankara, Turkey; A. Okay Celebi, Middle East Technical University, Mathematics Department, 06531 Ankara, Turkey

Abstract: In this paper we consider the equation
y"' + q(t){y'}^{\al} + p(t) h(y) =0,
where $p,q$ are real valued continuous functions on $[0,\iy)$ such that $q(t) \geq0$, $p(t) \geq0$ and $h(y)$ is continuous in $(-\iy,\iy)$ such that $h(y)y>0$ for $y \neq0$. We obtain sufficient conditions for solutions of the considered equation to be nonoscillatory. Furthermore, the asymptotic behaviour of these nonoscillatory solutions is studied.

Keywords: Third order nonlinear differential equations, nonoscillatory solutions, asymptotic properties of solutions

Classification (MSC 1991): 34C15, 34D05

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