Taiwanese Journal of Mathematics

Growth of Solutions of Higher Order Complex Linear Differential Equation

Jianren Long and Xiubi Wu

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Some new conditions on coefficient functions $A_{i}(z)$, which will guarantee all nontrivial solutions of $f^{(n)} + A_{n-1}(z) f^{(n-1)} + \cdots + A_{0}(z)f = 0$ are of infinite order, are found in this paper. The first condition involves two classes of extremal functions for some inequalities about finite asymptotic values and deficient values. The second condition assumes that a coefficient itself is a nontrivial solution of another differential equation $w'' + P(z)w = 0$, where $P(z)$ is a polynomial.

Article information

Taiwanese J. Math., Volume 21, Number 5 (2017), 961-977.

Received: 24 April 2016
Revised: 27 September 2016
Accepted: 8 January 2017
First available in Project Euclid: 1 August 2017

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 34M10: Oscillation, growth of solutions
Secondary: 30D35: Distribution of values, Nevanlinna theory

complex differential equation entire function infinite order Denjoy's conjecture Yang's inequality


Long, Jianren; Wu, Xiubi. Growth of Solutions of Higher Order Complex Linear Differential Equation. Taiwanese J. Math. 21 (2017), no. 5, 961--977. doi:10.11650/tjm/7950. https://projecteuclid.org/euclid.twjm/1501599178

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