## Bulletin of the Belgian Mathematical Society - Simon Stevin

- Bull. Belg. Math. Soc. Simon Stevin
- Volume 19, Number 4 (2012), 717-732.

### Further results on the exponent of convergence of zeros of solutions of certain higher order linear differential equations

Hong-Yan Xu and Jin Tu

#### Abstract

In this paper, we further investigate the exponent of convergence of the zero-sequence of solutions of the differential equation $$ f^{(k)}+a_{k-1}(z)f^{(k-1)}+\cdots+a_1(z)f' +\psi(z)f=0, $$ where $\psi(z)=\sum_{j=1}^\iota Q_j(z)e^{P_j(z)} (\iota\geq 3, \iota\in N_+ )$, $P_j(z)$ are polynomials of degree $n\geq1$, $Q_j(z),a_\Lambda(z)(\Lambda=1,2,\cdots,k-1;j=1,2,\ldots,\iota)$ are entire functions of order less than $n$, and $k\geq2$.

#### Article information

**Source**

Bull. Belg. Math. Soc. Simon Stevin, Volume 19, Number 4 (2012), 717-732.

**Dates**

First available in Project Euclid: 23 November 2012

**Permanent link to this document**

https://projecteuclid.org/euclid.bbms/1353695911

**Digital Object Identifier**

doi:10.36045/bbms/1353695911

**Mathematical Reviews number (MathSciNet)**

MR3009032

**Zentralblatt MATH identifier**

1271.34087

**Subjects**

Primary: 34A20 30D35: Distribution of values, Nevanlinna theory

**Keywords**

Linear differential equation entire function the exponent of convergence of zeros

#### Citation

Xu, Hong-Yan; Tu, Jin. Further results on the exponent of convergence of zeros of solutions of certain higher order linear differential equations. Bull. Belg. Math. Soc. Simon Stevin 19 (2012), no. 4, 717--732. doi:10.36045/bbms/1353695911. https://projecteuclid.org/euclid.bbms/1353695911