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

Volume 97 / 2010

Ting-Bin Cao, Zhong-Shu Deng Annales Polonici Mathematici 97 (2010), 51-61 MSC: Primary 34M10; Secondary 30D35. DOI: 10.4064/ap97-1-4

Abstract

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.

Authors

  • Ting-Bin CaoDepartment of Mathematics
    Nanchang University
    Nanchang 330031, China
    e-mail
  • Zhong-Shu DengEditorial office of Journal
    Nanchang University
    Nanchang 330047, China
    e-mail

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