Bulletin of the Belgian Mathematical Society - Simon Stevin

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

Hong-Yan Xu and Jin Tu

Full-text: Open access

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


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