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

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.