Commentarii Mathematici Helvetici


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Volume 79, Issue 3, 2004, pp. 451–470
DOI: 10.1007/s00014-003-0792-7

Published online: 2004-09-30

Estimates on the growth of meromorphic solutions of linear differential equations

Yik-Man Chiang[1] and Walter K. Hayman[2]

(1) Hong Kong University of Science and Technology, China
(2) Imperial College London, UK

We give a pointwise estimate of meromorphic solutions of linear differential equations with coefficients meromorphic in a finite disk or in the open plane. Our results improve some earlier estimates of Bank and Laine. In particular we show that the growth of meromorphic solutions with ()>0 can be estimated in terms of initial conditions of the solution at or near the origin and the characteristic functions of the coefficients. Examples show that the estimates are sharp in a certain sense. Our results give an affirmative answer to a question of Milne Anderson.

Keywords: linear differential equations, growth of meromorphic solutions, Nevanlinna characteristics

Chiang Yik-Man, Hayman Walter: Estimates on the growth of meromorphic solutions of linear differential equations. Comment. Math. Helv. 79 (2004), 451-470. doi: 10.1007/s00014-003-0792-7