Singular Cauchy Problem for an Ordinary Differential Equation Unsolved with Respect to the Derivative of the Unknown Function
- Authors: Zernov A.E.1, Kuzina Y.V.1
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Affiliations:
- Ushynskii South Ukrainian National Pedagogic University
- Issue: Vol 231, No 6 (2018)
- Pages: 712-729
- Section: Article
- URL: https://journals.rcsi.science/1072-3374/article/view/241224
- DOI: https://doi.org/10.1007/s10958-018-3846-5
- ID: 241224
Cite item
Abstract
For a singular Cauchy problem
where N ≥ 2 and aijk are constants, a00k = 0, k ∈ {0, 1, . . .,N} , a100 ≠ 0, a010 ≠ 0, aijk = 0, 1 ≤ i + j < m, k ∈ {1, . . . ,N} , 2 ≤ m ≤ N, and φ is a function small in a certain sense, we find a nonempty set of continuously differentiable solutions x: (0, ρ] → ℝ, where ρ is sufficiently small, such that
where c1, . . . , cm are known constants.
About the authors
A. E. Zernov
Ushynskii South Ukrainian National Pedagogic University
Email: Jade.Santos@springer.com
Ukraine, Staroportofrankovskaya Str. 26, Odessa, 65020
Yu. V. Kuzina
Ushynskii South Ukrainian National Pedagogic University
Email: Jade.Santos@springer.com
Ukraine, Staroportofrankovskaya Str. 26, Odessa, 65020