Article
Full entry |
PDF
(0.2 MB)
Feedback
PDF
(0.2 MB)
Feedback
Keywords:
linear differential equation; hyper-order; a finite singular point; Nevanlinna theory
linear differential equation; hyper-order; a finite singular point; Nevanlinna theory
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.
References:
[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 10.14492/hokmj/1381758109 | MR 0662294 | Zbl 0554.34003
[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 10.1360/02ys9031 | MR 1903625 | Zbl 1054.34139
[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 10.1016/S0252-9602(17)30359-4 | MR 2036062 | Zbl 1056.30029
[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 10.1007/s41980-020-00469-4 | MR 4329925 | Zbl 1474.34617
[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 10.46793/KgJMat2302.187C | MR 4592794 | Zbl 07721838
[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 3547415 | Zbl 1352.34113
[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 10.1016/j.jmaa.2017.10.005 | MR 3724712 | Zbl 1382.34097
[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 10.4153/CMB-1974-064-0 | MR 0385095 | Zbl 0314.30021
[9] Kwon, K.-H.: Nonexistence of finite order solutions of certain second order linear differential equations. Kodai Math. J. 19 (1996), 378-387. DOI 10.2996/kmj/1138043654 | MR 1418569 | Zbl 0879.34006
[10] Laine, I.: Nevanlinna Theory and Complex Differential Equations. de Gruyter Studies in Mathematics 15. Walter de Gruyter, Berlin (1993). DOI 10.1515/9783110863147 | MR 1207139 | Zbl 0784.30002
Search
Partner of
