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On asymptotic behavior of solutions of $n$-th order Emden-Fowler differential equations with advanced argument
Czechoslovak Mathematical Journal, Tome 60 (2010) no. 3, pp. 817-833 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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We study oscillatory properties of solutions of the Emden-Fowler type differential equation $$u^{(n)}(t)+p(t)\big |u(\sigma (t))\big |^\lambda \operatorname{sign} u(\sigma (t))=0,$$ where $0\lambda 1$, $p\in L_{\rm loc }(\Bbb R_+;\Bbb R)$, $\sigma \in C(\Bbb R_+;\Bbb R_+)$ and $\sigma (t)\ge t$ for $t\in \Bbb R_+$. \endgraf Sufficient (necessary and sufficient) conditions of new type for oscillation of solutions of the above equation are established. \endgraf Some results given in this paper generalize the results obtained in the paper by Kiguradze and Stavroulakis (1998).
We study oscillatory properties of solutions of the Emden-Fowler type differential equation $$u^{(n)}(t)+p(t)\big |u(\sigma (t))\big |^\lambda \operatorname{sign} u(\sigma (t))=0,$$ where $0\lambda 1$, $p\in L_{\rm loc }(\Bbb R_+;\Bbb R)$, $\sigma \in C(\Bbb R_+;\Bbb R_+)$ and $\sigma (t)\ge t$ for $t\in \Bbb R_+$. \endgraf Sufficient (necessary and sufficient) conditions of new type for oscillation of solutions of the above equation are established. \endgraf Some results given in this paper generalize the results obtained in the paper by Kiguradze and Stavroulakis (1998).
Classification : 34C10, 34K11, 34K15
Keywords: proper solution; property {\bf A}; property {\bf B} 
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Koplatadze, R. On asymptotic behavior of solutions of $n$-th order Emden-Fowler differential equations with advanced argument. Czechoslovak Mathematical Journal, Tome 60 (2010) no. 3, pp. 817-833. http://geodesic.mathdoc.fr/item/CMJ_2010_60_3_a14/

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