Geodesic
Asymptotic forms of solutions of perturbed half-linear ordinary differential equations
Archivum mathematicum, Tome 57 (2021) no. 1, pp. 27-39
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Asymptotic forms of solutions of half-linear ordinary differential equation $\big (|u^{\prime }|^{\alpha -1}u^{\prime }\big )^{\prime }= \alpha \big (1+b(t)\big ) |u|^{\alpha -1}u$ are investigated under a smallness condition and some signum conditions on $b(t)$. When $\alpha =1$, our results reduce to well-known ones for linear ordinary differential equations.
Asymptotic forms of solutions of half-linear ordinary differential equation $\big (|u^{\prime }|^{\alpha -1}u^{\prime }\big )^{\prime }= \alpha \big (1+b(t)\big ) |u|^{\alpha -1}u$ are investigated under a smallness condition and some signum conditions on $b(t)$. When $\alpha =1$, our results reduce to well-known ones for linear ordinary differential equations.
DOI : 10.5817/AM2021-1-27
Classification : 34A34, 34D05, 34E10
Keywords: half-linear ordinary differential equation; asymptotic form 
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Luey, Sokea; Usami, Hiroyuki. Asymptotic forms of solutions of perturbed half-linear ordinary differential equations. Archivum mathematicum, Tome 57 (2021) no. 1, pp. 27-39. doi: 10.5817/AM2021-1-27

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