STUDY OF PROPERTIES OF SOLUTIONS OF LINEAR DIFFERENTIAL EQUATIONS IN THE COMPLEX PLANE

Abstract

In this thesis, we are interested in studying the growth of solutions of higher-order linear di erential equations, speci cally focusing on conditions on coe cients under which the solutions of these equations are of in nite order. Firstly, we investigate the iterated order and iterated type of solutions of these equations where their coe cients are entire and meromorphic functions. Secondly, we study the hyper-order of analytic solutions of linear di erential equations whose coe cients are analytic near an isolated singular point. We also consider the non-homogeneous case. Finally, we use a new idea to estimate the growth of solutions of linear differential equations. We consider the coe cients of these equations as solutions of certain second-order linear di erential equations