Taiwanese Journal of Mathematics

THE INFINITE GROWTH OF SOLUTIONS OF COMPLEX DIFFERENTIAL EQUATIONS OF WHICH COEFFICIENT WITH DYNAMICAL PROPERTY

Guowei Zhang and Jian Wang

Full-text: Open access

Abstract

In this paper, we prove that the transcendental entire solution of complex linear differential equation $f^{(k)}-e^{P(z)}f=Q(z)$, where $P(z)$ is a transcendental entire function and $Q(z)$ is a polynomial, is of infinite hyper-order under the hypothesis that the Fatou set of $P(z)$ has a multiply connected component.

Article information

Source
Taiwanese J. Math., Volume 18, Number 4 (2014), 1063-1069.

Dates
First available in Project Euclid: 10 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1499706476

Digital Object Identifier
doi:10.11650/tjm.18.2014.3902

Mathematical Reviews number (MathSciNet)
MR3245429

Zentralblatt MATH identifier
1357.30019

Subjects
Primary: 30D05: Functional equations in the complex domain, iteration and composition of analytic functions [See also 34Mxx, 37Fxx, 39-XX] 30D35: Distribution of values, Nevanlinna theory

Keywords
complex differential equation Fatou set hyper-order

Citation

Zhang, Guowei; Wang, Jian. THE INFINITE GROWTH OF SOLUTIONS OF COMPLEX DIFFERENTIAL EQUATIONS OF WHICH COEFFICIENT WITH DYNAMICAL PROPERTY. Taiwanese J. Math. 18 (2014), no. 4, 1063--1069. doi:10.11650/tjm.18.2014.3902. https://projecteuclid.org/euclid.twjm/1499706476


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