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Nonoscillation and asymptotic behaviour for third order nonlinear differential equations

Aydın Tiryaki; A. Okay Çelebi — 1998

Czechoslovak Mathematical Journal

In this paper we consider the equation $y^{'''} + q (t) {y^{'}}^{α} + p (t) h (y) = 0,$ 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 $y \neq 0$ . We obtain sufficient conditions for solutions of the considered equation to be nonoscillatory. Furthermore, the asymptotic behaviour of these nonoscillatory solutions is studied.

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