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Growth of Solutions to Linear Differential Equations with Analytic Coefficients in a Punctured Disc

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Abstract

In this paper, we investigate the growth of solutions of the linear differential equation

$$f^{\left(k\right)}+A_{k-1}\left(z\right)\exp\left\{\frac{a_{k-1}}{z^{n}}\right\}f^{\left(k-1\right)}+...+A_{0}\left(z\right)\exp\left\{\frac{a_{0}}{z^{n}}\right\}f=F\left(z\right),$$

where \(A_{j}\left(z\right)\) are analytic functions in \(D\left(0,R\right)=\left\{z\in\mathbb{C}:0<\left|z\right|<R\right\}\) and \(a_{j}\ \left(j=0,...,k-1\right)\) are complex numbers. Under some conditions, we prove that every non trivial solution is of infinite order of growth near the singular point \(z=0\).

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ACKNOWLEDGMENTS

The authors would like to thank the referee for his/her time and useful comments towards the improvement of this paper.

Funding

This work is supported by University of Mostaganem (UMAB) and PRFU Project (Projet de Recherche Formation Universitaire, Code C00L03UN270120220005).

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Authors and Affiliations

  1. Laboratory of pure and applied mathematics, University of Mostaganem (UMAB), Mostaganem, Algeria

    S. Mazouz & S. Hamouda

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  1. S. Mazouz
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  2. S. Hamouda
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Correspondence to S. Mazouz or S. Hamouda.

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(Submitted by A. M. Elizarov)

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Mazouz, S., Hamouda, S. Growth of Solutions to Linear Differential Equations with Analytic Coefficients in a Punctured Disc. Lobachevskii J Math 43, 2230–2243 (2022). https://doi.org/10.1134/S199508022211021X

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  • DOI: https://doi.org/10.1134/S199508022211021X

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