For a singular Cauchy problem
where N ≥ 2 and a ijk are constants, a00k = 0, k ∈ {0, 1, . . .,N} , a100 ≠ 0, a010 ≠ 0, a ijk = 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, . . . , c m are known constants.
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Translated from Neliniini Kolyvannya, Vol. 20, No. 2, pp. 166–183, April–June, 2017.
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Zernov, A.E., Kuzina, Y.V. Singular Cauchy Problem for an Ordinary Differential Equation Unsolved with Respect to the Derivative of the Unknown Function. J Math Sci 231, 712–729 (2018). https://doi.org/10.1007/s10958-018-3846-5
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DOI: https://doi.org/10.1007/s10958-018-3846-5