Electronic Journal of Differential Equations,
Vol. 2015 (2015), No. 68, pp. 1-12.
Title: Oscillation of arbitrary-order derivatives of solutions to linear
differential equations taking small functions in the unit disc
Authors: Pan Gong (Jiangxi Normal Univ., Nanchang, China)
Li-Peng Xiao (Jiangxi Normal Univ., Nanchang, China)
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.