On Entire Solutions of Some Differential-Difference Equations

Abstract

In this paper, we will investigate the properties of entire solutions with finite order of the Fermat type difference or differential-difference equations. This is continuation of a recent paper (Liu et al. in Arch. Math. 99, 147–155, 2012). In addition, we also consider the value distribution and growth of the entire solutions of linear differential-difference equation \(f^{(k)}(z)=h(z)f(z+c),\) where \(h(z)\) is a non-zero meromorphic function, \(c\) is a non-zero constant. Our results partially answer the question given in Liu et al. (Arch. Math. 99, 147–155, 2012).