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) + Ak−1f(k−1) + ... + A2f ′′ + “D1 (z) + A1 (z) eP(z)” f ′ +“D0 (z) + A0 (z) eQ(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{ (Aj) (j = 0, 1, ..., k − 1) , (Dj ) (j = 0, 1)} < n. We also investigate the relationship between small functions and the solutions of the above equation.