Abstract:

In this paper, we study transcendental entire solutions of a certain type of complex differential-difference equations $\left[f(z)f'(z)\right]^{n}+f^{m}(z+\eta)=1,$ $\left[f(z)f'(z)\right]^{n}+[f(z+\eta)-f(z)]^{m}=1,$ $\left[f(z)f'(z)\right]^{2}+P^{2}(z)f^{2}(z+\eta)=Q(z)e^{\alpha(z)},$ where $P(z) $ and $Q(z) $ are non-zero polynomials, $\alpha(z) $ is polynomial, $ m$ and $n $ are positive integers, $ \eta\in{\Bbb C}\setminus\{0\}$. Several sufficient conditions on the non-existence of transcendental entire solutions of such equations are supplied.

Key words: Complex differential difference equation, Transcendental entire solution, Nevanlinna theory, Finite order