| Title:
|
Finite logarithmic order meromorphic solutions of linear difference/differential-difference equations (English) |
| Author:
|
Dahmani, Abdelkader |
| Author:
|
Belaïdi, Benharrat |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
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150 |
| Issue:
|
1 |
| Year:
|
2025 |
| Pages:
|
49-70 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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 (English) |
| Keyword:
|
linear difference equation |
| Keyword:
|
linear differential-difference equation |
| Keyword:
|
meromorphic function |
| Keyword:
|
logarithmic order |
| Keyword:
|
logarithmic lower order |
| MSC:
|
30D35 |
| MSC:
|
39A10 |
| MSC:
|
39B32 |
| DOI:
|
10.21136/MB.2024.0107-23 |
| . |
| Date available:
|
2025-02-20T16:08:49Z |
| Last updated:
|
2025-02-20 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/152875 |
| . |
| Reference:
|
[1] Belaïdi, B.: Growth of meromorphic solutions of finite logarithmic order of linear difference equations.Fasc. Math. 54 (2015), 5-20. Zbl 1331.39002, MR 3410127, 10.1515/fascmath-2015-0001 |
| Reference:
|
[2] Belaïdi, B.: Some properties of meromorphic solutions of logarithmic order to higher order linear difference equations.Bul. Acad. Ştiinţe Repub. Mold., Mat. 2017 (2017), 15-28. Zbl 1390.39008, MR 3683507 |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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