On Meromorphic Solutions of Non-linear Differential-Difference Equations

Abstract

Abstract In this paper, we investigate the non-existence of transcendental entire solutions for non-linear differential-difference equations of the forms $$\begin{aligned} f^{n}(z)+Q(z,f)=\beta _{1}e^{\alpha _{1}z}+\beta _{2}e^{\alpha _{2}z}+\cdots +\beta _{s}e^{\alpha _{s}z} \end{aligned}$$ f n ( z ) + Q ( z , f ) = β 1 e α 1 z + β 2 e α 2 z + ⋯ + β s e α s z and $$\begin{aligned} f^{n}(z)f^{(k)}(z)+L_d(z,f)=\sum ^{s}_{i=1}p_i(z)e^{\alpha _i{(z)}}, \end{aligned}$$ f n ( z ) f ( k ) ( z ) + L d ( z , f ) = ∑ i = 1 s p i ( z ) e α i ( z ) , where n , s are positive integers, $$n\ge s+2,$$ n ≥ s + 2 , Q ( z , f ) is a differential-difference polynomial in f of degree d .