GROWTH OF \(\varphi\)–ORDER SOLUTIONS OF LINEAR DIFFERENTIAL EQUATIONS WITH MEROMORPHIC COEFFICIENTS ON THE COMPLEX PLANE

Abstract

In this paper, we study the growth of solutions of higher order linear differential equations with meromorphic coefficients of \(\varphi\)-order on the complex plane. By considering the concepts of \(\varphi\)-order and \(\varphi \)-type, we will extend and improve many previous results due to Chyzhykov–Semochko, Belaïdi, Cao–Xu–Chen, Kinnunen.

Growth properties of solutions of complex differential equations with entire coefficients of finite (alpha,beta,gamma)-order

“…They used more general scale, called the ϕ-order (see [9]). In recent times, the concept of ϕ-order is used to study the growth of solutions of complex differential equations which extend and improve many previous results (see [4,5,9,19]).…”