On the growth of solutions of some non-homogeneous linear differential equations

Abstract

In this paper, we investigate the growth of solutions to the non-homogeneous linear di erential equation f(k) + Akð€€€1ebkð€€€1zf(kð€€€1) + + A1eb1zf 0 + A0eb0zf = Feaz; where Aj(z) 6 0 (j = 0; 1; : : : ; k ð€€€ 1), F(z) 6 0 are entire functions and a 6= 0, bj 6= 0 (j = 0; 1; : : : ; k ð€€€ 1) are complex numbers.