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The nature of the unit circle Differential Equations

Author: WangLi
Tutor: ChenZongZuo
School: South China Normal University
Course: Basic mathematics
Keywords: Unit disc Differential equations Growth order
CLC: O174.5
Type: Master's thesis
Year: 2007
Downloads: 43
Quote: 0
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Abstract


The linear differential equation of higher order in the unit disc is considered.Let f be a solution of homogeneous linear differential equation of higher order,and a sufficient condition for f to belong to the weighted Dirichlet space Dq or tothe Bergman space Lap, respectively, is obtained; and a sufficient condition for fto be non-admissible is also given. Let f be a solution of non-homogeneous lineardifferential equation of higher order fk+Ak-1(z)fk-1+…+A0(z)f=F(z),where Aj(z)(j=0,…, k-1), F(z)(?)0 are analytic in the unit disc, and therelation between the growth order of f and the growth orders of Aj(j=0,…, k-1)and F is obtained under different conditions.The algebraic differential equation f12=a0(z)(f-a1(z))2f, where a0(z) anda1(z) are analytic functions in the unit disc, is also considered. Let f be a solutionof the upper algebraic differential equation, and a sufficient condition for f tobelong to the weighted Hardy space Hq, where 2≤q≤∞, is given.

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CLC: > Mathematical sciences and chemical > Mathematics > Mathematical Analysis > Theory of functions > Complex analysis,complex function
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