2017
Том 69
№ 9

All Issues

Qualitative Investigation of the Singular Cauchy Problem $\sum\limits_{k = 1}^n {(a_{k1} t + a_{k2} x)(x')^k = b_1 t + b_2 x + f(t,x,x'),x(0) = 0}$

Zernov A. E.

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Abstract

We prove the existence of continuously differentiable solutions $x:(0,ρ] → R$ with required asymptotic properties as $t → +0$ and determine the number of these solutions.

English version (Springer): Ukrainian Mathematical Journal 55 (2003), no. 10, pp 1709–1715.

Citation Example: Zernov A. E. Qualitative Investigation of the Singular Cauchy Problem $\sum\limits_{k = 1}^n {(a_{k1} t + a_{k2} x)(x')^k = b_1 t + b_2 x + f(t,x,x'),x(0) = 0}$ // Ukr. Mat. Zh. - 2003. - 55, № 10. - pp. 1419-1424.

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