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

• Date: 2015
• Main Authors: Mokhonko, A. Z., Mokhonko, A. A., Мохонько, А. З., Мохонько, А. А.
• Format: Article
• Language: English
• Published: Institute of Mathematics, NAS of Ukraine 2015
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/1969
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

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...