Abstract:

In this paper, we study the structure of meromorphic solutions of the nonlinear differential-difference equations $ f^n(z)f^{(k)}(z)+q(z){\rm e}^{Q(z)}f(z+c)=P(z) $, where $ n $ and $ k $ are positive integers, $ q(z) $ and $ Q(z) $ are nonzero polynomials with $ \deg Q\geq 1 $, and $ P(z) $ is an entire function of order less than $ \deg Q $. By using the Nevanlinna theory and the estimates on the module of logarithmic derivative, we prove that the above equations do posses special exponential polynomial solutions.

Key words: differential-difference equation, meromorphic solution, entire function, exponential polynomial