@article{Zernov_Chaichuk_2005, title={Qualitative investigation of a singular Cauchy problem for a functional differential equation}, volume={57}, url={https://umj.imath.kiev.ua/index.php/umj/article/view/3690}, abstractNote={We consider the singular Cauchy problem
$$txprime(t) = f(t,x(t),x(g(t)),xprime(t),xprime(h(t))), x(0) = 0,$$
where $x: (0, τ) → ℝ, g: (0, τ) → (0, + ∞), h: (0, τ) → (0, + ∞), g(t) ≤ t$, and $h(t) ≤ t, t ∈ (0, τ)$, for linear, perturbed linear, and nonlinear equations. In each case, we prove that there exists a nonempty set of continuously differentiable solutions $x: (0, ρ] → ℝ$ ($ρ$ is sufficiently small) with required asymptotic properties.}, number={10}, journal={Ukrains’kyi Matematychnyi Zhurnal}, author={Zernov, A. E. and Chaichuk, O. R.}, year={2005}, month={Oct.}, pages={1344–1358} }