Asymptotic Behavior of Solutions of the Cauchy Problem x′ = f(t, x, x′), x(0) = 0

• Date: 2002
• Main Authors: Zernov, A. E., Kuzina, Yu. V., Зєрнов, А. Є., Кузіна, Ю. В.
• Format: Article
• Language: Ukrainian; English
• Published: Institute of Mathematics, NAS of Ukraine 2002
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/4209
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

We prove the existence of continuously differentiable solutions \(x:(0,{\rho ]} \to \mathbb{R}^n\) such that $$\left\| {x\left( t \right) - {\xi }\left( t \right)} \right\| = O\left( {{\eta }\left( t \right)} \right),{ }\left\| {x'\left( t \right) - {\xi '}\left( t \right)} \...