A question of Gol'dberg and Ostrovskii concerning linear differential equations with coefficients of completely regular growth

TL;DR

This paper demonstrates that linear differential equations with coefficients of completely regular growth can have finite order entire solutions that are not of completely regular growth, answering a question posed by Gol'dberg and Ostrovskii.

Contribution

It provides a counterexample showing the existence of solutions with different growth properties than their coefficients, addressing an open question.

Findings

Existence of finite order solutions not of completely regular growth

Coefficients of completely regular growth do not guarantee similar growth in solutions

Answers a longstanding question in complex differential equations

Abstract

We show that a linear differential equation whose coefficients are entire functions of completely regular growth may have an entire solution of finite order which is not of completely regular growth. This answers a question of Gol'dberg and Ostrovskii.