Growth of solutions of certain non-homogeneous linear differential equations with entire coefficients

Abstract

In this paper, we investigate the growth of solutions of the differential equation f (k)+ Ak− 1 (z) f (k− 1)+···+ A1 (z) f+ A0 (z) f= F, where A0 (z),..., Ak− 1 (z), F (z)/≡ 0 are entire functions, and we obtain general estimates of the hyperexponent of convergence of distinct zeros and the hyper-order of solutions for the above equation.