Entire Solutions Of Certain Non-Linear Differential-Difference Equations

TL;DR

This paper investigates the existence and non-existence of finite order transcendental entire solutions for specific nonlinear differential-difference equations, addressing conjectures by Rong et al. and Chen et al.

Contribution

It provides new results on the conditions for solutions and resolves some conjectures in the field of nonlinear differential-difference equations.

Findings

Established criteria for existence of solutions.

Proved non-existence under certain conditions.

Addressed and confirmed conjectures by Rong et al. and Chen et al.

Abstract

In this paper, we study about existence and non-existence of finite order transcendental entire solutions of the certain non-linear differential-difference equations. We also study about conjectures posed by Rong et al. and Chen et al.