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

Benharrat Belaïdi ; Zinelâabidine Latreuch

Mathematica Moravica, Tome 17 (2013) no. 1.

Résumé

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 $\Delta$.

Détail

Mots-clés : Linear differential equations, Polynomial of solutions, Meromorphic solutions, Iterated order, Iterated exponent of convergence of the sequence of distinct zeros, Unit disc