Entire Solutions for Certain Class of Non-Linear General Difference Equations

Abstract

In this paper, we investigate the entire solutions for a certain class of non-linear difference equations of the form: $f^n+ q(z)e^{Q(z)}\mathcal{L}_1(z, f)$ $= α_1(z)e^{β_1(z)}+α_2(z)e^{ β_2(z)},$ where $\mathcal{L}_1(z, f)$ is the generalized linear difference operator, $α_1(z)$ and $α_2(z)$ are non-zero small functions of $f,$ $q(z)$ and $Q(z)$(nonconstant), $β_1(z)$ and $β_2(z)$ are non-zero polynomials. Our results improve upon and generalize some previously established findings.