Geodesic
Nonoscillation and asymptotic behaviour for third order nonlinear differential equations
Czechoslovak Mathematical Journal, Tome 48 (1998) no. 4, pp. 677-685 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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In this paper we consider the equation \[y^{\prime \prime \prime } + q(t){y^{\prime }}^{\alpha } + p(t) h(y) =0,\] where $p,q$ are real valued continuous functions on $[0,\infty )$ such that $q(t) \ge 0$, $p(t) \ge 0$ and $h(y)$ is continuous in $(-\infty ,\infty )$ such that $h(y)y>0$ for $y \ne 0$. We obtain sufficient conditions for solutions of the considered equation to be nonoscillatory. Furthermore, the asymptotic behaviour of these nonoscillatory solutions is studied.
In this paper we consider the equation \[y^{\prime \prime \prime } + q(t){y^{\prime }}^{\alpha } + p(t) h(y) =0,\] where $p,q$ are real valued continuous functions on $[0,\infty )$ such that $q(t) \ge 0$, $p(t) \ge 0$ and $h(y)$ is continuous in $(-\infty ,\infty )$ such that $h(y)y>0$ for $y \ne 0$. We obtain sufficient conditions for solutions of the considered equation to be nonoscillatory. Furthermore, the asymptotic behaviour of these nonoscillatory solutions is studied.
Classification : 34C10, 34C15, 34D05
Keywords: Third order nonlinear differential equations; nonoscillatory solutions; asymptotic properties of solutions 
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Tiryaki, Aydın; Çelebi, A. Okay. Nonoscillation and asymptotic behaviour for third order nonlinear differential equations. Czechoslovak Mathematical Journal, Tome 48 (1998) no. 4, pp. 677-685. http://geodesic.mathdoc.fr/item/CMJ_1998_48_4_a5/

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