an:05631645
Zbl 1199.34471
Cao, Tingbin; Yi, Hongxun
On the complex oscillation theory of linear differential equations with analytic coefficients in the unit disc
ZH
Acta Math. Sci., Ser. A, Chin. Ed. 28, No. 6, 1046-1057 (2008).
00255408
2008
j
34M10 30D35 34M03
linear differential equation; analytic function; complex oscillation theory; unit disc
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.