Complex Oscillation Theory of Differential Polynomials

Abstract

In this paper, we investigate the relationship between small functions and differential polynomials gf (z) = d2f

+ d1f

+ d0f, where d0(z), d1(z), d2(z) are entire functions that are not all equal to zero with ρ(dj) < 1 (j = 0, 1, 2) generated by solutions of the differential equation f

+ A1(z)eazf

+ A0(z)ebzf = F, where a, b are complex numbers that satisfy ab(a − b) = 0 and Aj(z) ≡ 0 (j = 0, 1), F(z) ≡ 0 are entire functions such that max {ρ(Aj), j = 0, 1, ρ(F)} < 1.