Proceedings of the Japan Academy, Series A, Mathematical Sciences

Finite order meromorphic solutions of linear difference equations

Sheng Li and Zong-Sheng Gao

Full-text: Open access

Abstract

In this paper, we mainly investigate the growth and the value distribution of meromorphic solutions of the linear difference equation \begin{equation*} a_{n}(z)f(z+n)+…+a_{1}(z)f(z+1)+a_{0}(z)f(z)=b(z), \end{equation*} where $a_{0}(z),a_{1}(z),\cdots,a_{n}(z),b(z)$ are entire functions such that $a_{0}(z)a_{n}(z)\not\equiv 0$. For a finite order meromorphic solution $f(z)$, some interesting results on the relation between $\rho=\rho(f)$ and $\lambda_{f}=\max\{\lambda(f),\lambda(1/f)\}$, are proved. And examples are provided for our results.

Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 87, Number 5 (2011), 73-76.

Dates
First available in Project Euclid: 26 April 2011

Permanent link to this document
https://projecteuclid.org/euclid.pja/1303825550

Digital Object Identifier
doi:10.3792/pjaa.87.73

Mathematical Reviews number (MathSciNet)
MR2803894

Zentralblatt MATH identifier
1226.30032

Subjects
Primary: 30D35: Distribution of values, Nevanlinna theory 39A13: Difference equations, scaling ($q$-differences) [See also 33Dxx] 39A22: Growth, boundedness, comparison of solutions

Keywords
Difference equations value distribution finite order

Citation

Li, Sheng; Gao, Zong-Sheng. Finite order meromorphic solutions of linear difference equations. Proc. Japan Acad. Ser. A Math. Sci. 87 (2011), no. 5, 73--76. doi:10.3792/pjaa.87.73. https://projecteuclid.org/euclid.pja/1303825550


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