Linear differential equations with entire coefficients having the same order and type

Abstract

In this article, we study the growth of solutions to the differential equation $$ f^{k}+(A_{k-1}(z)e^{P_{k-1}(z)}e^{lambda z^m} +B_{k-1}(z))f^{k-1}+dots +(A_0(z)e^{P_0(z)} e^{lambda z^m}+B_0(z))f=0, $$ where $lambda in mathbb{C}^{ast}$, $mgeq 2$ is an integer and $max_{j=0,dots ,k-1}{ deg P_j(z)} <m$, $A_j,B_j$ $(j=0,dots ,k-1)$ are entire functions of orders less than m.

Keywords

• Linear differential equations
• growth of solutions
• hyper-order