Solutions of non-homogeneous linear differential equations in the unit disc
Annales Polonici Mathematici, Tome 97 (2010) no. 1, pp. 51-61.

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The main purpose of this paper is to consider the analytic solutions of the non-homogeneous linear differential equation $$ f^{(k)}+a_{k-1}(z)f^{(k-1)}+ \cdots + a_{1}(z)f'+a_{0}(z)f=F(z), $$ where all coefficients $a_{0},$ $a_{1},\ldots,a_{k-1},F\not\equiv 0$ are analytic functions in the unit disc $\mathbb{D}=\{z\in\mathbb{C}: |z|1\}.$ We obtain some results classifying the growth of finite iterated order solutions in terms of the coefficients with finite iterated type. The convergence exponents of zeros and fixed points of solutions are also investigated.
DOI : 10.4064/ap97-1-4
Keywords: main purpose paper consider analytic solutions non homogeneous linear differential equation k k cdots z where coefficients ldots k equiv analytic functions unit disc mathbb mathbb obtain results classifying growth finite iterated order solutions terms coefficients finite iterated type convergence exponents zeros fixed points solutions investigated

Ting-Bin Cao 1 ; Zhong-Shu Deng 2

1 Department of Mathematics Nanchang University Nanchang 330031, China
2 Editorial office of Journal Nanchang University Nanchang 330047, China
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Ting-Bin Cao; Zhong-Shu Deng. Solutions of non-homogeneous linear differential equations
in the unit disc. Annales Polonici Mathematici, Tome 97 (2010) no. 1, pp. 51-61. doi : 10.4064/ap97-1-4. http://geodesic.mathdoc.fr/articles/10.4064/ap97-1-4/

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