Abstract
We prove the existence of continuously differentiable solutions \(x:(0,\rho ] \to {\mathbb{R}}\) with required asymptotic properties as t → +0 and determine the number of these solutions.
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Zernov, A.E., Kuzina, Y.V. Qualitative Investigation of the Singular Cauchy Problem \(\sum\limits_{k = 1}^n {(a_{k1} t + a_{k2} x)(x')^k = b_1 t + b_2 x + f(t,x,x'),x(0) = 0} \) . Ukrainian Mathematical Journal 55, 1709–1715 (2003). https://doi.org/10.1023/B:UKMA.0000022075.68820.4e
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DOI: https://doi.org/10.1023/B:UKMA.0000022075.68820.4e