Growth and oscillation of some class of differential polynomials in the unit disc

Abstract

In this paper , we study the growth and the oscillation of complex di erential equations f00 + A1(z)f0 + A0(z)f = 0 and f00 + A1(z)f0 + A0(z)f = F; where A0 6 0;A1 and F are analytic functions in the unit disc = fz :j z j< 1g with nite iterated p- order . We obtain some results on the iterated p􀀀 order and the iterated exponent of convergence of zero - points in of the di erential polynomials gf = d1f0 + d0f and gf = d1f0 + d0f + b; where d1; d0; b are analytic functions such that at least one of d0(z); d1(z) does not vanish identically with p(dj) < 1 (j = 0; 1); p(b) < 1: