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Zbl 1080.34503
Zernov, A.E.; Kuzina, Yu.V.
Qualitative investigation of the singular Cauchy problem $\sum_{k=1}^n (a_{k1}t+a_{k2} x)(x')^k=b_1t+b_2x+f(t,x,x'),x(0)=0$.
(Russian, English)
[J] Ukr. Mat. Zh. 55, No. 10, 1419-1424 (2003); translation in Ukr. Math. J. 55, No. 10, 1709-1715 (2003). ISSN 0041-6053

Summary: We prove the existence of continuously differentiable solutions $x\colon (0, \rho]\to\Bbb R$ with required asymptotic properties as $t\to+0$ and determine the number of these solutions.
MSC 2000:
*34A09 Implicit equations
34A12 Initial value problems for ODE
34D05 Asymptotic stability of ODE

Keywords: singular Cauchy problem; existence of solution

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