Asymptotic forms of solutions of perturbed half-linear ordinary differential equations
- 1 January 2021
- journal article
- research article
- Published by Masaryk University Press in Archivum Mathematicum
- Vol. 57 (1), 27-39
- https://doi.org/10.5817/am2021-1-27
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
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