Geodesic
On the hyper-order of analytic solutions of linear differential equations near a finite singular point
Mathematica Bohemica, Tome 149 (2024) no. 4, pp. 569-583
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

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.
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.
DOI : 10.21136/MB.2024.0075-23
Classification : 30D35, 34M10
Keywords: linear differential equation; hyper-order; a finite singular point; Nevanlinna theory 
@article{10_21136_MB_2024_0075_23,
     author = {Chetti, Meryem and Hamani, Karima},
     title = {On the hyper-order of analytic solutions of linear differential equations near a finite singular point},
     journal = {Mathematica Bohemica},
     pages = {569--583},
     year = {2024},
     volume = {149},
     number = {4},
     doi = {10.21136/MB.2024.0075-23},
     mrnumber = {4840085},
     zbl = {07980806},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/MB.2024.0075-23/}
}
TY  - JOUR
AU  - Chetti, Meryem
AU  - Hamani, Karima
TI  - On the hyper-order of analytic solutions of linear differential equations near a finite singular point
JO  - Mathematica Bohemica
PY  - 2024
SP  - 569
EP  - 583
VL  - 149
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.21136/MB.2024.0075-23/
DO  - 10.21136/MB.2024.0075-23
LA  - en
ID  - 10_21136_MB_2024_0075_23
ER  - 
%0 Journal Article
%A Chetti, Meryem
%A Hamani, Karima
%T On the hyper-order of analytic solutions of linear differential equations near a finite singular point
%J Mathematica Bohemica
%D 2024
%P 569-583
%V 149
%N 4
%U http://geodesic.mathdoc.fr/articles/10.21136/MB.2024.0075-23/
%R 10.21136/MB.2024.0075-23
%G en
%F 10_21136_MB_2024_0075_23
Chetti, Meryem; Hamani, Karima. On the hyper-order of analytic solutions of linear differential equations near a finite singular point. Mathematica Bohemica, Tome 149 (2024) no. 4, pp. 569-583. doi: 10.21136/MB.2024.0075-23

[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. | DOI | MR | JFM

[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. | DOI | MR | JFM

[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. | DOI | MR | JFM

[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. | DOI | MR | JFM

[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. | DOI | MR | JFM

[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. | MR | JFM

[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. | DOI | MR | JFM

[8] Hayman, W. K.: The local growth of power series: A survey of the Wiman-Valiron method. Can. Math. Bull. 17 (1974), 317-358. | DOI | MR | JFM

[9] Kwon, K.-H.: Nonexistence of finite order solutions of certain second order linear differential equations. Kodai Math. J. 19 (1996), 378-387. | DOI | MR | JFM

[10] Laine, I.: Nevanlinna Theory and Complex Differential Equations. de Gruyter Studies in Mathematics 15. Walter de Gruyter, Berlin (1993). | DOI | MR | JFM

Cité par Sources :