Exponential polynomialsas solutions of non-linear differential-difference equations

Abstract

Exponential polynomials, an important subclass of finite order entire functions, as solutions of differential or difference or differential-difference equations are considered in [5, 10, 19, 20]. The critical domains of zeros and the quotients of exponential polynomials are considered in [6]. In this paper, we proceed to consider the exponential polynomials as solutions of some general complex differential-difference equations and extend existence results.