On asymptotics of solutions of one Cauchy’s problem

• Date: 2025
• Main Authors: Zernov , A. E., Зернов , А. Е.
• Format: Article
• Language: Russian
• Published: Institute of Mathematics, NAS of Ukraine 2025
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/9355
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

We consider the Cauchy problem $(x')^n=at^r+bx+f(t,x,x'), x(0)=0$. We prove the existence of continuously differentiable solutions and study their asymptotic behavior for $t→+0$.