Growth Properties of Solutions to Higher Order Complex Linear Differential Equations with Analytic Coefficients in the Annulus
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Дифференциальные, интегральные и другие функциональные уравнения. Конечные разности. Вариационное исчисление. Функциональный анализ (252)
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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


Rezumat

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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