On the complex oscillation theory of linear differential equations with analytic coefficients in the unit disc. (Chinese. English summary) Zbl 1199.34471

Cao, Tingbin; Yi, Hongxun

Acta Math. Sci., Ser. A, Chin. Ed. 28, No. 6, 1046-1057 (2008).

Summary: The complex oscillation theory of linear differential equations of the form \[ L (f)=f^{ (k)}+A_{k-1} (z)f^{ (k-1)}+\cdots +A_0 (z)f=F (z)\;(k\in {\mathbb N}) \] is investigated, where the coefficients \(A_j (z)\) \((j=0,\ldots, k-1)\) and \(F (z)\) are analytic functions in the unit disc \(\Delta=\{z\,:\,|z|<1\}\). 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.

MSC:

34M10	Oscillation, growth of solutions to ordinary differential equations in the complex domain
30D35	Value distribution of meromorphic functions of one complex variable, Nevanlinna theory
34M03	Linear ordinary differential equations and systems in the complex domain

Keywords:

linear differential equation; analytic function; complex oscillation theory; unit disc