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 '' + A(1)e(P(z)) f' + A(0)e(Q(z)) f = 0, where P(z) = a(n)z(n) + ... + a(0), Q(z) = b(n)z(n) + ... + b(0) are polynomials with degree n (n >= 1), a(i), b(i) (i = 0, 1,..., n), a(n)b(n) not equal 0 are complex constants, A(j) (z) not equivalent to 0 (j = 0, 1) are entire functions with sigma(A(j)) < n.