Meromorphic solutions of some type of system of differential and difference equations

YANG Yan-yan; WEI Wen-long; HUANG Zhi-gang

doi:10.3969/j.issn.1000-5641.2018.01.006

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YANG Yan-yan, WEI Wen-long, HUANG Zhi-gang. Meromorphic solutions of some type of system of differential and difference equations[J]. Journal of East China Normal University (Natural Sciences), 2018, (1): 50-58. doi: 10.3969/j.issn.1000-5641.2018.01.006

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YANG Yan-yan, WEI Wen-long, HUANG Zhi-gang. Meromorphic solutions of some type of system of differential and difference equations[J]. Journal of East China Normal University (Natural Sciences), 2018, (1): 50-58. doi: 10.3969/j.issn.1000-5641.2018.01.006

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Meromorphic solutions of some type of system of differential and difference equations

doi: 10.3969/j.issn.1000-5641.2018.01.006

College of Mathematics and Physics, Suzhou University of Science and Technology, Suzhou Jiangsu 215009, China

Received Date: 2017-02-27
Publish Date: 2018-01-25

Abstract

Abstract

This article investigates some properties of meromorphic solutions of the type of system of differential-difference equations of the following form $\begin{eqnarray*}\begin{cases}f_1^n-p_1(z)f_2(z+c)=h_1(z), \ \\f_2^n-p_2(z)f_1(z+c)=h_2(z)\end{cases}\end{eqnarray*}$ where n ≥ 4, p₁(z)、p₂(z) are non-zero polynomials, and h₁(z), h₂(z) are entire functions. By using Nevanlinna theorem, we have obtained the solution of above equation is unique. We also discuss the conditions for several types of system of differential-difference equations if the systems of equations actually pose meromorphic solutions of finite order.
- Nevanlinna theory,
- system of equations,
- differential-difference equation,
- meromorphic solution

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References(8)

References

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