## Bulletin of the Belgian Mathematical Society - Simon Stevin

- Bull. Belg. Math. Soc. Simon Stevin
- Volume 20, Number 1 (2013), 27-39.

### On the hyper-order of solutions of a class of higher order linear differential equations

Karima Hamani and Benharrat Belaïdi

#### Abstract

In this paper, we investigate the growth of solutions of the linear differential equation \begin{multline*} f^{(k)}+\left( A_{k-1}(z)e^{P_{k-1}(z)}+B_{k-1}\left( z\right) \right) f^{(k-1)}+\cdots +\\\left( A_{1}(z)e^{P_{1}(z)}+B_{1}\left( z\right) \right) f^{\prime } +\left( A_{0}(z)e^{P_{0}(z)}+B_{0}\left( z\right) \right) f=0, \end{multline*} where $k\geq 2$\ is an integer, $P_{j}(z)$ $(j=0,1,\cdots ,k-1)$\ are nonconstant polynomials\ and $A_{j}(z)$ $\left( \not\equiv 0\right) ,$ $ B_{j}\left( z\right) $\ $\left( \not\equiv 0\right) $ $(j=0,1,\cdots ,k-1)$\ are meromorphic functions. Under some conditions, we determine the hyper-order of these solutions.

#### Article information

**Source**

Bull. Belg. Math. Soc. Simon Stevin, Volume 20, Number 1 (2013), 27-39.

**Dates**

First available in Project Euclid: 18 April 2013

**Permanent link to this document**

https://projecteuclid.org/euclid.bbms/1366306712

**Mathematical Reviews number (MathSciNet)**

MR3082741

**Zentralblatt MATH identifier**

1278.34101

**Subjects**

Primary: 34M10: Oscillation, growth of solutions 30D35: Distribution of values, Nevanlinna theory

**Keywords**

Linear differential equation meromorphic function hyper-order

#### Citation

Hamani, Karima; Belaïdi, Benharrat. On the hyper-order of solutions of a class of higher order linear differential equations. Bull. Belg. Math. Soc. Simon Stevin 20 (2013), no. 1, 27--39. https://projecteuclid.org/euclid.bbms/1366306712