Fast growing solutions of linear differential equations with analytic coefficients in the unit disc

Author:

Kara Mohamed Abdelhak, ,Belaïdi BenharratORCID,

Abstract

In this paper, we investigate the growth of solutions of higher order linear differential equations with analytic coefficients of ϕ-order in the unit disc. We introduce new definitions of the lower order and the type related to the ϕ-order concepts to generalise and extend previous results due to Chyzhykov-Semochko [6], Semochko [14], Belaïdi [1,2,3], Hu-Zheng [12].

Publisher

University of Craiova

Subject

Computer Science Applications,General Mathematics

Reference16 articles.

1. "[1] B. Belaïdi, Growth of solutions to linear differential equations with analytic coefficients of [p, q] -order in the unit disc, Electron. J. Differential Equations 2011(2011), No. 156, 11 pp.

2. [2] B. Belaïdi, Growth of ρϕ -order solutions of linear differential equations with entire coefficients, PanAmer. Math. J. 27(2017), no. 4, 26-42.

3. [3] B. Belaïdi, Fast growing solutions to linear differential equations with entire coefficients having the same ρϕ-order, J. of Math. and Applications 42(2019), 63-77.

4. [4] T.B. Cao and H.X. Yi, The growth of solutions of linear differential equations with coefficients of iterated order in the unit disc, J. Math. Anal. Appl. 319(2006), no. 1, 278-294.

5. [5] I. Chyzhykov, G. G. Gundersen, and J. Heittokangas, Linear differential equations and logarithmic derivatives estimates, Proc. London Math. Soc. 86(2003), no. 3, 735-754.

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