On the growth of solutions of a class of higher order linear differential equations with coefficients having the same order

Abstract

In this paper, the authors investigate the growth of solutions of a class of higher order linear differential equationswhen most coefficients in the above equations have the same order with each other, and obtain some results which improve previous results due to K.H. Kwon [K.H. Kwon, Nonexistence of finite order solutions of certain second order linear differential equations, Kodai Math.

Nonhomogeneous linear differential equations with entire coefficients having the same order and type

“…Several authors studied the case when the coefficients have the same order. In 2008, Tu and Yi investigated the growth of solutions of the homogeneous equation (2) when most coefficients have the same order, see [8]. Next, in 2009, Wang and Laine improved this work to nonhomogeneous equation (1) by proving the following result.…”

Study of solutions of logarithmic order to higher order linear differential-difference equations with coeffcients having the same logarithmic order

“…In [16], Tu and Yi investigated the growth of solutions of a class of higher order linear differential equations with entire coefficients when most of them are of the same order, and obtained the following result.…”

Complex Oscillation of Higher-Order Linear Differential Equations with Coefficients Being Lacunary Series of Finite Iterated Order

“…What can we have if there exists one middle coefficient ( ) (1 ≤ ≤ −1) such that ( ) grows faster than other coefficients in (12) or (13)? Many authors have investigated this question when ( ) is of finite order and obtained many results (e.g., see [13][14][15]). Here, our question is that under what conditions can we obtain similar results with Theorems B-C if ( ) (1 ≤ ≤ − 1) is of finite iterated order and grows faster than other coefficients in (12) or (13).…”