Bulletin of the Belgian Mathematical Society - Simon Stevin

Growth of solutions of some higher order linear difference equations

Xiaoguang Qi, Zhenhua Wang, and Lianzhong Yang

Full-text: Open access

Abstract

This paper is devoted to studying the growth of solutions of equations of type $f(z+n)+\sum_{j=0}^{n-1}\{P_{j}(e^{z})+Q_{j}(e^{-z})\}f(z+j)=0$ and $f(z+n)+ \sum_{j=0}^{n-1}\{P_{j}(e^{A(z)})+Q_{j}(e^{-A(z)})\}f(z+j)=0$, where $P_{j}(z)$ and $Q_{j}(z)$ are polynomials in $z$ and $A(z)$ is a transcendental entire function. We prove three theorems of such type, which improve some results in [6,7].

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 20, Number 1 (2013), 111-122.

Dates
First available in Project Euclid: 18 April 2013

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1366306717

Digital Object Identifier
doi:10.36045/bbms/1366306717

Mathematical Reviews number (MathSciNet)
MR3082746

Zentralblatt MATH identifier
1283.39005

Subjects
Primary: 39A05: General theory
Secondary: 30D35: Distribution of values, Nevanlinna theory

Keywords
Meromorphic functions Difference equation Finite order

Citation

Qi, Xiaoguang; Wang, Zhenhua; Yang, Lianzhong. Growth of solutions of some higher order linear difference equations. Bull. Belg. Math. Soc. Simon Stevin 20 (2013), no. 1, 111--122. doi:10.36045/bbms/1366306717. https://projecteuclid.org/euclid.bbms/1366306717


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