Entire Solutions for Certain Class of Non-Linear General Difference Equations (Journal of Nonlinear Modeling and Analysis, 2025)
In this paper, we investigate the entire solutions for a certainclass 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 improveupon and generalize some previously established findings.
Keywords: Non-linear difference equations; meromorphic function; entire solution; Nevanlinna theory.