Relations between Solutions of Differential Equations and Small Functions

Abstract

We investigate relations between solutions, their derivatives of differential equationf(k)+Ak−1f(k−1)+⋯+A1f’+A0f=0, and functions of small growth, whereAj  (j=0,1,…,k−1)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.