ON ENTIRE SOLUTIONS OF CERTAIN TYPE OF DIFFERENTIAL-DIFFERENCE EQUATIONS

Abstract

In this paper, we deal with differential-difference equations of the form $$ f(z)^2+p(z)f(z+c)+h(z)f'(z)+g(z)=d_1e^{\lambda z}+d_2e^{-\lambda z} $$ where $p(z),~ h(z),~ g(z)$ are polynomials, and $c,~ d_1,~d_2, ~\lambda\in \mathbb{C}$ are constants with $d_1 d_2\lambda\not= 0$. By utilizing Nevanlinna's value distribution theory, some sufficient conditions on the nonexistence of entire solutions regarding the equations are provided.