ON THE GROWTH OF SOLUTIONS OF HOMOGENEOUS AND NON-HOMOGENEOUS LINEAR DIFFERENTIAL EQUATIONS WITH MEROMORPHIC COEFFICIENTS

Abstract

In this paper, we investigate the growth of solutions of higher order linear differential equations f (k)+ Ak− 1 (z) f (k− 1)+···+ A1 (z) f+ A0 (z) f= 0 and f (k)+ Ak− 1 (z) f (k− 1)+···+ A1 (z) f+ A0 (z) f= F (z), where A0 (z)≡ 0, A1 (z),···, Ak− 1 (z) and F (z)≡ 0 are meromorphic functions of finite iterated p-order. We improve and extend some results of papers [1] and [5] by using the concept of the iterated order and considering the growth of some arbitrary dominant coefficient As (s= 0, 1,···, k− 1) instead of A0.