Relations between Solutions of Differential Equations and Small Functions

Abstract

We investigate relations between solutions, their derivatives of differential equation $f^{\left(k\right)}+A_{k-1}{f}^{\left(k-1\right)}+\cdots +A_1{f}^{’}+A_{0}f=0$, and functions of small growth, where $A_j\left(j=0,1,\dots ,k-1\right)$ are entire functions of finite order. By these relations, we see that every transcendental solution and its derivative of above equation have infinitely many fixed points.