Electron. J. Diff. Equ., Vol. 2015 (2015), No. 68, pp. 1-12.

Oscillation of arbitrary-order derivatives of solutions to linear differential equations taking small functions in the unit disc

Pan Gong, Li-Peng Xiao

Abstract:
In this article, we study the relationship between solutions and their derivatives of the differential equation
$$ f''+A(z)f'+B(z)f=F(z), $$
where $A(z), B(z), F(z)$ are meromorphic functions of finite iterated p-order in the unit disc. We obtain some oscillation theorems for $f^{(j)}(z)-\varphi(z)$, where f is a solution and $\varphi(z)$ is a small function.

Submitted January 6, 2015. Published March 20, 2015.
Math Subject Classifications: 34M10, 30D35.
Key Words: Unit disc; iterated order; growth; exponent of convergence.

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Pan Gong
Institute of Mathematics and Information Science
Jiangxi Normal University
Nanchang 330022, China
email: gongpan12@163.com
Li Peng Xiao
Institute of Mathematics and Information Science
Jiangxi Normal University
Nanchang 330022, China
email: 2992507211@qq.com

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