2017
Том 69
№ 6

All Issues

On the Order of Growth of the Solutions of Linear Differential Equations in the Vicinity of a Branching Point

Mokhon'ko A. Z., Mokhon'ko O. A.


Abstract

Assume that the coefficients and solutions of the equation $f^{(n)}+p_{n−1}(z)f^{(n−1)} +...+ p_{s+1}(z)f^{(s+1)} +...+ p_0(z)f = 0$ have a branching point at infinity (e.g., a logarithmic singularity) and that the coefficients $p_j , j = s+1, . . . ,n−1$, increase slower (in terms of the Nevanlinna characteristics) than $p_s(z)$. It is proved that this equation has at most $s$ linearly independent solutions of finite order.

English version (Springer): Ukrainian Mathematical Journal 67 (2015), no. 1, pp 159-165.

Citation Example: Mokhon'ko A. Z., Mokhon'ko O. A. On the Order of Growth of the Solutions of Linear Differential Equations in the Vicinity of a Branching Point // Ukr. Mat. Zh. - 2015. - 67, № 1. - pp. 139-144.