Abstract:

The complex oscillation theory of linear differential equations of the form L(f)=f^(k)+A_k-1(z)f^{(k-1)₊ …} + A₀(z)f=F(z)(k∈ N) is investigated, where the coefficients A_j(z) (j=0, ^… , k-1) and F(z) are analytic functions in the unit disc △={z:|z|<1}. The authors obtain several precise theorems about the hyper order, the hyper convergence exponent of zero points and fixed points of solutions of differential equations.

Key words: Linear differential equation, Analytic function, Complex oscillation theory, Unit disc