GROWTH OF SOLUTIONS OF HIGHER ORDER LINEAR DIFFERENTIAL EQUATIONS

This paper is devoted to studying the growth of solutions of the higher order nonhomogeneous linear differential equation f^(k) + A_k−1f^(k−1) + ... + A₂f " + (D₁ (z) + A₁ (z) e^P(z)) f ' + (D₀ (z) + A₀ (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.