The exact entire solutions of certain type of nonlinear difference equations · arXivDesk2007.12311Jul 24, 2020Entire solution, Nevanlinna theory, Difference equations, Riccati equation
The exact entire solutions of certain type of nonlinear difference equations
Feng Lü, Cuiping Li, Junfeng Xu
Abstract
In this paper, we consider the entire solutions of nonlinear difference equation f3+q(z)Δf=p1eα1z+p2eα2z
where
is a polynomial, and
p1,p2,α1,α2 are nonzero constants with
. It is showed that if
is a non-constant entire solution of
to the above equation, then
f(z)=e1e3α1z+e2e3α2z, where
and
are two constants. Meanwhile, we give an affirmative answer to the conjecture posed by Zhang et al in [18].