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October, 2017 Growth of Solutions of Higher Order Complex Linear Differential Equation
Jianren Long, Xiubi Wu
Taiwanese J. Math. 21(5): 961-977 (October, 2017). DOI: 10.11650/tjm/7950

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.

Citation

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Jianren Long. Xiubi Wu. "Growth of Solutions of Higher Order Complex Linear Differential Equation." Taiwanese J. Math. 21 (5) 961 - 977, October, 2017. https://doi.org/10.11650/tjm/7950

Information

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

zbMATH: 06871354
MathSciNet: MR3707879
Digital Object Identifier: 10.11650/tjm/7950

Subjects:
Primary: 34M10
Secondary: 30D35

Rights: Copyright © 2017 The Mathematical Society of the Republic of China

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Vol.21 • No. 5 • October, 2017
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