Growth of solutions of higher order linear differential equations

Abstract

This paper is devoted to studying the growth of solutions of the higher order nonhomogeneous linear differential equation f (k)+ A k− 1 f (k− 1)+...+ A 2 f"+(D 1 (z)+ A 1 (z) e P (z)) f'+(D 0 (z)+ A 0 (z) e Q (z)) f= F (k≥ 2), where P (z), Q (z) are nonconstant polynomials such that deg P= degQ= n and Aj (z)(j= 0, 1,..., k− 1), F (z) are entire functions with max {p (Aj)(j= 0, 1,..., k− 1), p (Dj)(j= 0, 1)}< n. We also investigate the relationship between small functions and the solutions of the above equation.