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

Ting-Bin Cao; Zhong-Shu Deng

Annales Polonici Mathematici, Tome 98 (2010), p. 51-61 / Harvested from The Polish Digital Mathematics Library

Résumé

The main purpose of this paper is to consider the analytic solutions of the non-homogeneous linear differential equation $f^{(k)} + a_{k - 1} (z) f^{(k - 1)} + \dots + a ₁ (z) f^{'} + a ₀ (z) f = F (z)$ , where all coefficients $a ₀, a ₁, . . ., a_{k - 1}$ , 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.

Publié le : 2010-01-01

Zbl 1192.34102

EUDML-ID : urn:eudml:doc:280259

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     year = {2010},
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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 98 (2010) pp. 51-61. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap97-1-4/