| Title:
|
On the hyper-order of analytic solutions of linear differential equations near a finite singular point (English) |
| Author:
|
Chetti, Meryem |
| Author:
|
Hamani, Karima |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
149 |
| Issue:
|
4 |
| Year:
|
2024 |
| Pages:
|
569-583 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We study the hyper-order of analytic solutions of linear differential equations with analytic coefficients having the same order near a finite singular point. We improve previous results given by S. Cherief and S. Hamouda (2021). We also consider the nonhomogeneous linear differential equations. (English) |
| Keyword:
|
linear differential equation |
| Keyword:
|
hyper-order |
| Keyword:
|
a finite singular point |
| Keyword:
|
Nevanlinna theory |
| MSC:
|
30D35 |
| MSC:
|
34M10 |
| DOI:
|
10.21136/MB.2024.0075-23 |
| . |
| Date available:
|
2024-12-13T19:07:03Z |
| Last updated:
|
2024-12-13 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/152680 |
| . |
| Reference:
|
[1] Amemiya, I., Ozawa, M.: Non-existence of finite order solutions of $\omega''+e^{-z}\omega'+Q(z)\omega=0$.Hokkaido Math. J. 10 (1981), 1-17. Zbl 0554.34003, MR 0662294, 10.14492/hokmj/1381758109 |
| Reference:
|
[2] Chen, Z.: The growth of solutions of $f''+e^{-z}f'+Q(z)f=0$, where the order $(Q)=1$.Sci China, Ser. A 45 (2002), 290-300. Zbl 1054.34139, MR 1903625, 10.1360/02ys9031 |
| Reference:
|
[3] Chen, Z., Shon, K.: On the growth of solutions of a class of higher order differential equations.Acta Math. Sci., Ser. B, Engl. Ed. 24 (2004), 52-60. Zbl 1056.30029, MR 2036062, 10.1016/S0252-9602(17)30359-4 |
| Reference:
|
[4] Cherief, S., Hamouda, S.: Linear differential equations with analytic coefficients having the same order near a singular point.Bull. Iran. Math. Soc. 47 (2021), 1737-1749. Zbl 1474.34617, MR 4329925, 10.1007/s41980-020-00469-4 |
| Reference:
|
[5] Cherief, S., Hamouda, S.: Growth of solutions of a class of linear differential equations near a singular point.Kragujevac J. Math. 47 (2023), 187-201. Zbl 07721838, MR 4592794, 10.46793/KgJMat2302.187C |
| Reference:
|
[6] Fettouch, H., Hamouda, S.: Growth of local solutions to linear differential around an isolated essential singularity.Electron. J. Diff. Equs. 2016 (2016), Article ID 226, 10 pages. Zbl 1352.34113, MR 3547415 |
| Reference:
|
[7] Hamouda, S.: The possible orders of growth of solutions to certain linear differential equations near a singular points.J. Math. Anal. Appl. 458 (2018), 992-1008. Zbl 1382.34097, MR 3724712, 10.1016/j.jmaa.2017.10.005 |
| Reference:
|
[8] Hayman, W. K.: The local growth of power series: A survey of the Wiman-Valiron method.Can. Math. Bull. 17 (1974), 317-358. Zbl 0314.30021, MR 0385095, 10.4153/CMB-1974-064-0 |
| Reference:
|
[9] Kwon, K.-H.: Nonexistence of finite order solutions of certain second order linear differential equations.Kodai Math. J. 19 (1996), 378-387. Zbl 0879.34006, MR 1418569, 10.2996/kmj/1138043654 |
| Reference:
|
[10] Laine, I.: Nevanlinna Theory and Complex Differential Equations.de Gruyter Studies in Mathematics 15. Walter de Gruyter, Berlin (1993). Zbl 0784.30002, MR 1207139, 10.1515/9783110863147 |
| . |
