Electron. J. Diff. Equ., Vol. 2015 (2015), No. 283, pp. 1-11.

Exponent of convergence of solutions to linear differential equations in the unit disc

Nacera Berrighi, Saada Hamouda

Abstract:
In this article, we study the exponent of convergence of $f^{(i) }-\varphi $ where $f\not\equiv 0$ is a solution of linear differential equations with analytic and meromorphic coefficients in the unit disc and $\varphi $ is a small function of $f$. From this results we deduce the fixed points of $f^{(i) }$ by taking $\varphi(z) =z$. We will see the similarities and differences between the complex plane and the unit disc.

Submitted May 21, 2015. Published November 11, 2015.
Math Subject Classifications: 34M10, 30D35.
Key Words: Linear differential equations; exponent of convergence; growth of solutions, unit disc.

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Nacera Berrighi
Laboratory of Pure and Applied Mathematics
University of Mostaganem, UMAB, Algeria
email: berrighinacera@univ-mosta.dz
Saada Hamouda
Laboratory of Pure and Applied Mathematics
University of Mostaganem, UMAB, Algeria
email: hamoudasaada@univ-mosta.dz, hamouda_saada@yahoo.fr

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