Meromorphic Solutions of Homogeneous and Non-homogeneous Higher Order Linear Difference Equations in Terms of (p,q)-Order

TL;DR

This paper studies the growth behavior of meromorphic solutions to higher order linear difference equations, introducing (p,q)-order concepts to refine existing growth estimates for solutions with entire or meromorphic coefficients.

Contribution

It extends previous results by applying (p,q)-order and (p,q)-lower order techniques to better understand the growth of solutions to difference equations.

Findings

Improved bounds on the order of meromorphic solutions.

Extended results on growth estimates using (p,q)-order.

Enhanced understanding of solution behavior in difference equations.

Abstract

In this paper we investigate the growth of meromorphic solutions of homogeneous and non-homogeneous linear difference equations with entire or meromorphic coefficients. We further extend and improve few results on the order of meromorphic solutions by using (p,q)-lower order and (p,q)-lower type followed by the investigation of Luo and Zheng (2016), Belaidi and Bellaama (2020).