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

Sokea Luey and Hiroyuki Usami

Address:
Sokea Luey, Graduate School of Engineering, Gifu University, Gifu 501-1193, Japan
Hiroyuki Usami, Faculty of Engineering, Gifu University, Gifu 501-1193, Japan

E-mail:
lueysokea2013.sl@gmail.com
husami@gifu-u.ac.jp

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.

AMSclassification: primary 34E10; secondary 34D05, 34A34.

Keywords: half-linear ordinary differential equation, asymptotic form.

DOI: 10.5817/AM2021-1-27