Qualitative Investigation of the Singular Cauchy Problem $\sum\limits_{k = 1}^n {(a_{k1} t + a_{k2} x)(x')^k = b_1 t + b_2 x + f(t,x,x'),x(0) = 0}$

Authors

  • A. E. Zernov

Abstract

We prove the existence of continuously differentiable solutions $x:(0,ρ] → R$ with required asymptotic properties as $t → +0$ and determine the number of these solutions.

Published

25.10.2003

Issue

Section

Short communications

How to Cite

Zernov, A. E. “Qualitative Investigation of the Singular Cauchy Problem $\sum\limits_{k = 1}^n {(a_{k1} T + a_{k2} x)(x’)^k = b_1 T + b_2 X + f(t,x,x’),x(0) = 0}$”. Ukrains’kyi Matematychnyi Zhurnal, vol. 55, no. 10, Oct. 2003, pp. 1419-24, https://umj.imath.kiev.ua/index.php/umj/article/view/4010.