Relations between the Small Functions and the Solutions of Certain Second-order Differential Equations

In this paper, we investigate the relations between the small functions and the solutions, first, second derivatives, and differential polynomial of the solutions to the differential equation f ′′ +A1e P f ′ +A0e f = 0, where P (z) = anz + · · · + a0, Q(z) = bnz + · · · + b0 are polynomials with degree n (n ≥ 1), ai, bi (i = 0, 1, . . . , n), anbn 6= 0 are complex constants, Aj(z) 6≡ 0 (j = 0, 1) are entire functions with σ(Aj) < n.