Fast growing solutions of linear differential equations with analytic coefficients in the unit disc

Abstract

In this paper, we investigate the growth of solutions of higher order linear differential equations with analytic coefficients of ϕ-order in the unit disc. We introduce new definitions of the lower order and the type related to the ϕ-order concepts to generalise and extend previous results due to Chyzhykov-Semochko [6], Semochko [14], Belaïdi [1,2,3], Hu-Zheng [12].