Growth and Oscillation of Polynomial of Linearly Independent Meromorphic Solutions of Second Order Linear Differential Equations in the Unit Disc

Benharrat Belaïdi, Zinelâabidine Latreuch

In this paper, we deal with the growth and oscillation of $w = d_{1}f_{1} + d_{2}f_{2}$, where $d_{1}$, $d_{2}$ are meromorphic functions of finite iterated $p$-order that are not all vanishing identically and $f_{1}$, $f_{2}$ are two linearly independent meromorphic solutions in the unit disc $\Delta = \{z \in C: |z| < 1\}$ satisfying $\delta (\infty,f_{j}) > 0$, $(j = 1, 2)$, of the linear differential equation $f'' + A(z)f = 0$, where $A(z)$ is admissible meromorphic function of finite iterated $p$-order in $\Delta$.