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

### 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.
Published

25.01.2015

How to Cite

*Ukrains’kyi Matematychnyi Zhurnal*, Vol. 67, no. 1, Jan. 2015, pp. 139-44, http://umj.imath.kiev.ua/index.php/umj/article/view/1969.

Issue

Section

Short communications