Growth Properties of Solutions to Higher Order Complex Linear Differential Equations with Analytic Coefficients in the Annulus

Belaidi Benharrat

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251

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2024-08-18 14:28

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517.91 (11)

Ecuații diferențiale. Ecuații integrale. Alte ecuații funcționale. Diferențe finite. Calculul variațional. Analiză funcțională (246)

SM ISO690:2012

BELAIDI, Benharrat. Growth Properties of Solutions to Higher Order Complex Linear Differential Equations with Analytic Coefficients in the Annulus. In: Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, 2023, nr. 2(102), pp. 19-35. ISSN 1024-7696. DOI: https://doi.org/10.56415/basm.y2023.i2.p19

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Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica

Numărul 2(102) / 2023 / ISSN 1024-7696 /ISSNe 2587-4322

Growth Properties of Solutions to Higher Order Complex Linear Differential Equations with Analytic Coefficients in the Annulus

DOI:https://doi.org/10.56415/basm.y2023.i2.p19

CZU: 517.91

Pag. 19-35

Belaidi Benharrat

Department of Mathematics, University of Mostaganem (UMAB)

Disponibil în IBN: 29 noiembrie 2023

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In this paper, by using the Nevanlinna value distribution theory of meromorphic functions on an annulus, we deal with the growth properties of solutions of the linear differential equation f(k)+Bk−1 (z) f(k−1)+· · ·+B1 (z) f0+B0 (z) f = 0, where k ≥ 2 is an integer and Bk−1 (z) , ...,B1 (z) ,B0 (z) are analytic on an annulus. Under some conditions on the coefficients, we obtain some results concerning the estimates of the order and the hyper-order of solutions of the above equation. The results obtained extend and improve those of Wu and Xuan in [16].

Cuvinte-cheie
and phrases: linear differential equations, analytic solutions, annulus, hyper order

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