Growth and oscillation of solutions to linear differential equations with entire coefficients having the same order

Abstract

In this article, we investigate the growth and fixed points of solutions of the differential equation $$ f^{(k)}+A_{k-1}(z)f^{(k-1)}+dots +A_{1}(z)f'+A_{0}(z)f=0, $$ where $A_{0}(z),dots$, $A_{k-1}(z)$ are entire functions. Some estimates are given for the iterated order and iterated exponent of convergence of fixed points of solutions of the above equation when most of the coefficients have the same order with each other.

Keywords

• Linear differential equation
• growth of entire function
• iterated order