Solutions of non-homogeneous linear differential equations in the unit disc

Ting-Bin Cao¹ ; Zhong-Shu Deng²

¹ Department of Mathematics Nanchang University Nanchang 330031, China
² Editorial office of Journal Nanchang University Nanchang 330047, China

Annales Polonici Mathematici, Tome 97 (2010) no. 1, pp. 51-61.

Résumé

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.

Détail

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