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

  • A. Z. Mokhonko
  • A. A. Mokhonko

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
MokhonkoA. Z., and MokhonkoA. A. “On the Order of Growth of the Solutions of Linear Differential Equations in the Vicinity of a Branching Point”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 67, no. 1, Jan. 2015, pp. 139-44, http://umj.imath.kiev.ua/index.php/umj/article/view/1969.
Section
Short communications