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

Ting-Bin Cao, and Zhong-Shu Deng. "Solutions of non-homogeneous linear differential equations in the unit disc." Annales Polonici Mathematici 97.1 (2010): 51-61. <http://eudml.org/doc/280259>.

@article{Ting2010,
abstract = {The main purpose of this paper is to consider the analytic solutions of the non-homogeneous linear differential equation $f^\{(k)\} + a_\{k-1\}(z)f^\{(k-1)\} + ⋯ + a₁(z)f^\{\prime \} + a₀(z)f = F(z)$, where all coefficients $a₀,a₁,...,a_\{k-1\}$, F ≢ 0 are analytic functions in the unit disc = z∈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.},
author = {Ting-Bin Cao, Zhong-Shu Deng},
journal = {Annales Polonici Mathematici},
keywords = {linear differential equation; analytic solutions; iterated order},
language = {eng},
number = {1},
pages = {51-61},
title = {Solutions of non-homogeneous linear differential equations in the unit disc},
url = {http://eudml.org/doc/280259},
volume = {97},
year = {2010},
}

TY - JOUR
AU - Ting-Bin Cao
AU - Zhong-Shu Deng
TI - Solutions of non-homogeneous linear differential equations in the unit disc
JO - Annales Polonici Mathematici
PY - 2010
VL - 97
IS - 1
SP - 51
EP - 61
AB - The main purpose of this paper is to consider the analytic solutions of the non-homogeneous linear differential equation $f^{(k)} + a_{k-1}(z)f^{(k-1)} + ⋯ + a₁(z)f^{\prime } + a₀(z)f = F(z)$, where all coefficients $a₀,a₁,...,a_{k-1}$, F ≢ 0 are analytic functions in the unit disc = z∈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.
LA - eng
KW - linear differential equation; analytic solutions; iterated order
UR - http://eudml.org/doc/280259
ER -