On the fast growth of solutions to higher order linear differential equations with entire coefficients connection

Saidani Mansouria ; Benharrat Belaïdi 

Novi Sad Journal of Mathematics, Tome 46 (2016) no. 2.

Résumé

In this paper, we investigate the iterated order of solutions of higher order homogeneous and nonhomogeneous 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 $A_{0}\left( z\right) \not\equiv 0,A_{1}\left( z\right) ,\cdots ,A_{k}\left( z\right) \not\equiv 0$ and $F\left( z\right) \not\equiv 0$ are entire functions of finite iterated $p-$order. We improve and extend some results of He, Zheng and Hu; Long and Zhu by using the concept of the iterated order and we obtain general estimates of the iterated convergence exponent and the iterated $p$-order of solutions for the above equations.

Détail

Publié le : 2016-08-13

DOI : 10.30755/NSJOM.04529

Classification : 34M10, 30D35
Keywords: linear differential equations, meromorphic function, iterated order