| Title:
|
On the meromorphic solutions of a certain type of nonlinear difference-differential equation (English) |
| Author:
|
Majumder, Sujoy |
| Author:
|
Mahato, Lata |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
148 |
| Issue:
|
1 |
| Year:
|
2023 |
| Pages:
|
73-94 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The main objective of this paper is to give the specific forms of the meromorphic solutions of the nonlinear difference-differential equation $$ f^{n}(z)+P_{d}(z,f)=p_{1}(z){\rm e}^{\alpha _{1}(z)}+p_{2}(z){\rm e}^{\alpha _{2}(z)}, $$ where $P_d(z,f)$ is a difference-differential polynomial in $f(z)$ of degree $d\leq n-1$ with small functions of $f(z)$ as its coefficients, $p_1$, $p_2$ are nonzero rational functions and $\alpha _1$, $\alpha _2$ are non-constant polynomials. More precisely, we find out the conditions for ensuring the existence of meromorphic solutions of the above equation. (English) |
| Keyword:
|
nonlinear differential equation |
| Keyword:
|
differential polynomial |
| Keyword:
|
Nevanlinna's value distribution theory |
| MSC:
|
30D30 |
| MSC:
|
30D35 |
| MSC:
|
33E30 |
| MSC:
|
34M05 |
| idZBL:
|
Zbl 07655814 |
| idMR:
|
MR4536311 |
| DOI:
|
10.21136/MB.2022.0186-20 |
| . |
| Date available:
|
2023-02-03T11:22:27Z |
| Last updated:
|
2023-09-13 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/151528 |
| . |
| 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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| 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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| . |
