Dual exponential polynomials and linear differential equations

We study linear differential equations with exponential polynomial coefficients, where exactly one coefficient is of order greater than all the others. The main result shows that a nontrivial exponential polynomial solution of such an equation has a certain dual relationship with the maximum order c...

Full description

Saved in:
Bibliographic Details
Published in:Journal of Differential Equations 2018-01, Vol.264 (1), p.98-114
Main Authors: Wen, Zhi-Tao, Gundersen, Gary G., Heittokangas, Janne
Format: Article
Language:English
Subjects:
Dual exponential polynomials
Entire function
Exponential polynomial
Finite order solution
Linear differential equation
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We study linear differential equations with exponential polynomial coefficients, where exactly one coefficient is of order greater than all the others. The main result shows that a nontrivial exponential polynomial solution of such an equation has a certain dual relationship with the maximum order coefficient. Several examples illustrate our results and exhibit possibilities that can occur.
ISSN:0022-0396
1090-2732
DOI:10.1016/j.jde.2017.09.003