Geodesic
Exponent of convergence of solutions of LDE in the unit disc
Novi Sad Journal of Mathematics, Tome 47 (2017) no. 1.

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In this paper, we investigate the exponent of convergence of $f^{\left( i\right) }-\varphi $ where $f^{\left( 0\right) }=f\not\equiv 0$ is a solution of linear differential equations with meromorphic coefficients in the unit disc and $\varphi $ is a small function of $f$. Our investigation is based on the behavior of the coefficients in a subset $\Gamma $ of the unit disc such that the set $\Gamma _{0}=\left\{ \left\vert z\right\vert :z\in \Gamma \right\} $ is of infinite logarithmic measure. By this investigation we can deduce the fixed points of $f^{\left( i\right) } $ by taking $\varphi \left( z\right) =z$.
Publié le :
DOI : 10.30755/NSJOM.04656
Classification : 34M10, 30D35
Keywords: linear differential equations, exponent of convergence of solutions, unit disc 
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     title = {Exponent of convergence of solutions of {LDE} in the unit disc},
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     year = {2017},
     doi = {10.30755/NSJOM.04656},
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Yssaad Somia; Saada Hamouda. Exponent of convergence of solutions of LDE in the unit disc. Novi Sad Journal of Mathematics, Tome 47 (2017) no. 1. doi : 10.30755/NSJOM.04656. http://geodesic.mathdoc.fr/articles/10.30755/NSJOM.04656/

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