### Asymptotic forms of solutions of perturbed half-linear ordinary differential equations

Sokea Luey, Hiroyuki Usami
Published: 1 January 2021

Abstract: 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.
Keywords: perturbed / prime / ordinary differential / Asymptotic / signum / forms of solutions / half linear ordinary

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