Open AccessSome Properties on The [p,q]-Order of Meromorphic Solutions of Homogeneous and Non-homogeneous Linear Differential Equations With Meromorphic Coefficients
Author(s) -
Mansouria Saidani,
Benharrat Belaïdi
Publication year - 2021
Publication title -
european journal of mathematical analysis
Language(s) - English
Resource type - Journals
ISSN - 2733-3957
DOI - 10.28924/ada/ma.1.86
Subject(s) - meromorphic function , order (exchange) , homogeneous , mathematics , prime (order theory) , left and right , homogeneous differential equation , differential equation , combinatorics , mathematical analysis , ordinary differential equation , differential algebraic equation , structural engineering , finance , engineering , economics
In the present paper, we investigate the $\left[p,q\right] $-order of solutions of higher order linear differential equations\begin{equation*}A_{k}\left(z\right) f^{\left( k\right) }+A_{k-1}\left( z\right) f^{\left(k-1\right)}+\cdots +A_{1}\left( z\right) f^{\prime }+A_{0}\left( z\right) f=0\end{equation*}and\begin{equation*}A_{k}\left( z\right) f^{\left( k\right) }+A_{k-1}\left( z\right) f^{\left(k-1\right) }+\cdots +A_{1}\left( z\right) f^{\prime }+A_{0}\left( z\right) f=F\left( z\right),\end{equation*}where $A_{0}\left( z\right) ,$ $A_{1}\left( z\right) ,...,A_{k}\left(z\right) \not\equiv 0$ and $F\left( z\right) \not\equiv 0$ are meromorphic functions of finite $\left[ p,q\right] $-order. We improve and extend some results of the authors by using the concept $\left[ p,q\right] $-order.