TY - JOUR
T1 - Entire Solutions for Certain Class of Non-Linear General Difference Equations
AU - Waghamore , Harina P.
AU - B. E. , Manjunath
JO - Journal of Nonlinear Modeling and Analysis
VL - 4
SP - 1240
EP - 1253
PY - 2025
DA - 2025/07
SN - 7
DO - http://doi.org/10.12150/jnma.2025.1240
UR - https://global-sci.org/intro/article_detail/jnma/24233.html
KW - Non-linear difference equations, meromorphic function, entire solution, Nevanlinna theory.
AB - <p style="text-align: justify;">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.</p>