Riccati differential equations with elliptic coefficients. II
type: Item
instance of: scholarly article
title: Riccati differential equations with elliptic coefficients. II
zbMATH Open document ID: 1088.34074
author: Katsuya Ishizaki
author: Ilpo Laine
author: Shun Shimomura
author: Kazuya Tohge
published in: Tôhoku Mathematical Journal. Second Series
publication date: 2004-02-11T00:00:00Z
review text: The authors continue their study of solutions of the Riccati differential equation of form \(w' + w^2 +a\wp(z)=0\) [Result. Math. 38, 58--71 (2000; Zbl 0954.34076)]. They modify slightly the Weierstrass \(\wp\)-function and obtain results which are analogies to the previous. It gives us an idea, when \(m\) is an odd integer, there are no logarithmic singularities [\textit{N. V. Grigorenko}, Math. Notes 33, 453--454 (1983); translation from Mat. Zametki 33, No. 6, 881--884 (1983; Zbl 0549.34005) and Math. Notes 51, No. 6, 627 (1992); translation from Mat. Zametki 51, No. 6, 155 (1992; Zbl 0792.34005)] in solutions of the equation for any choice of the Weierstrass \(\wp\)-function. Moreover the associated operator \(y''+ +a\wp(z)y\) is algebro-geometric [\textit{R. Weikard}, Electron. J. Differ. Equ. 2000, Paper No. 19 (2000; Zbl 0953.34073)].
Mathematics Subject Classification ID: 34M05
Mathematics Subject Classification ID: 34A34
zbMATH DE Number: 2040358
reviewed by: Mykola Grygorenko
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2748/tmj/1113247448
OpenAlex ID: W2043868410
cites work: On a theorem of Picard
cites work: Q4112233
cites work: Riccati differential equations with elliptic coefficients
cites work: Nevanlinna theory and complex differential equations
cites work: Q4368855
DOI: 10.2748/TMJ/1113247448
description: scientific article; zbMATH DE number 2040358