## Taiwanese Journal of Mathematics

### Growth of Solutions of Higher Order Complex Linear Differential Equation

#### Abstract

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

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

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

https://projecteuclid.org/euclid.twjm/1501599178

Digital Object Identifier
doi:10.11650/tjm/7950

Mathematical Reviews number (MathSciNet)
MR3707879

Zentralblatt MATH identifier
06871354

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

#### Citation

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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