Finite logarithmic order meromorphic solutions of linear difference/differential-difference equations

Abdelkader Dahmani; Benharrat Belaidi

Mathematica Bohemica (2025)

  • Issue: 1, page 49-70
  • ISSN: 0862-7959

Abstract

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Firstly we study the growth of meromorphic solutions of linear difference equation of the form$$ A_{k}(z)f(z+c_{k})+\cdots +A_{1}(z)f(z+c_{1})+A_{0}(z)f(z)=F(z), $$ where $A_{k}(z),\ldots ,A_{0}(z)$ and $F(z)$ are meromorphic functions of finite logarithmic order, $c_{i}$ $(i=1,\ldots ,k, k\in \mathbb {N})$ are distinct nonzero complex constants. Secondly, we deal with the growth of solutions of differential-difference equation of the form $$ \sum _{i=0}^{n}\sum _{j=0}^{m}A_{ij}(z)f^{(j)}(z+c_{i})=F(z), $$ where $A_{ij}(z)$ $(i=0,1,\ldots ,n, j=0,1,\ldots ,m,n, m\in \mathbb {N})$ and $F(z)$ are meromorphic functions of finite logarithmic order, $c_{i}$ $(i=0,\ldots ,n)$ are distinct complex constants. We extend some previous results obtained by Zhou and Zheng and Biswas to the logarithmic lower order.\looseness -1

How to cite

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Dahmani, Abdelkader, and Belaidi, Benharrat. "Finite logarithmic order meromorphic solutions of linear difference/differential-difference equations." Mathematica Bohemica (2025): 49-70. <http://eudml.org/doc/299895>.

@article{Dahmani2025,
abstract = {Firstly we study the growth of meromorphic solutions of linear difference equation of the form$$ A\_\{k\}(z)f(z+c\_\{k\})+\cdots +A\_\{1\}(z)f(z+c\_\{1\})+A\_\{0\}(z)f(z)=F(z), $$ where $A_\{k\}(z),\ldots ,A_\{0\}(z)$ and $F(z)$ are meromorphic functions of finite logarithmic order, $c_\{i\}$ $(i=1,\ldots ,k, k\in \mathbb \{N\})$ are distinct nonzero complex constants. Secondly, we deal with the growth of solutions of differential-difference equation of the form $$ \sum \_\{i=0\}^\{n\}\sum \_\{j=0\}^\{m\}A\_\{ij\}(z)f^\{(j)\}(z+c\_\{i\})=F(z), $$ where $A_\{ij\}(z)$ $(i=0,1,\ldots ,n, j=0,1,\ldots ,m,n, m\in \mathbb \{N\})$ and $F(z)$ are meromorphic functions of finite logarithmic order, $c_\{i\}$ $(i=0,\ldots ,n)$ are distinct complex constants. We extend some previous results obtained by Zhou and Zheng and Biswas to the logarithmic lower order.\looseness -1},
author = {Dahmani, Abdelkader, Belaidi, Benharrat},
journal = {Mathematica Bohemica},
language = {eng},
number = {1},
pages = {49-70},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Finite logarithmic order meromorphic solutions of linear difference/differential-difference equations},
url = {http://eudml.org/doc/299895},
year = {2025},
}

TY - JOUR
AU - Dahmani, Abdelkader
AU - Belaidi, Benharrat
TI - Finite logarithmic order meromorphic solutions of linear difference/differential-difference equations
JO - Mathematica Bohemica
PY - 2025
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
IS - 1
SP - 49
EP - 70
AB - Firstly we study the growth of meromorphic solutions of linear difference equation of the form$$ A_{k}(z)f(z+c_{k})+\cdots +A_{1}(z)f(z+c_{1})+A_{0}(z)f(z)=F(z), $$ where $A_{k}(z),\ldots ,A_{0}(z)$ and $F(z)$ are meromorphic functions of finite logarithmic order, $c_{i}$ $(i=1,\ldots ,k, k\in \mathbb {N})$ are distinct nonzero complex constants. Secondly, we deal with the growth of solutions of differential-difference equation of the form $$ \sum _{i=0}^{n}\sum _{j=0}^{m}A_{ij}(z)f^{(j)}(z+c_{i})=F(z), $$ where $A_{ij}(z)$ $(i=0,1,\ldots ,n, j=0,1,\ldots ,m,n, m\in \mathbb {N})$ and $F(z)$ are meromorphic functions of finite logarithmic order, $c_{i}$ $(i=0,\ldots ,n)$ are distinct complex constants. We extend some previous results obtained by Zhou and Zheng and Biswas to the logarithmic lower order.\looseness -1
LA - eng
UR - http://eudml.org/doc/299895
ER -

References

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