Fast Growing Solutions to Linear Differential Equations with Entire Coefficients Having the Same ρφ-order

Abstract

: This paper deals with the growth of solutions of a class of higher order linear differential equations when most coefficients A j ( z ) ( j = 0 , ..., k − 1) have the same ρ ϕ -order with each other. By using the concept of τ ϕ -type, we obtain some results which indicate growth estimate of every non-trivial entire solution of the above equations by the growth estimate of the coefficient A 0 ( z ) . We im-prove and generalize some recent results due to Chyzhykov-Semochko and the author.