Riccati differential equations with elliptic coefficients
type: Item
instance of: scholarly article
title: Riccati differential equations with elliptic coefficients
zbMATH Open document ID: 0954.34076
DOI: 10.1007/BF03322431
author: Katsuya Ishizaki
author: Ilpo Laine
author: Shun Shimomura
author: Kazuya Tohge
published in: Results in Mathematics
publication date: 2000-08-31T00:00:00Z
review text: In this paper, the authors consider the Riccati differential equation \[ w'+w^2+a\wp(z)=0, \] where \(\wp(z)\) is the Weierstrass \(\wp\)-function satisfying \[ (\wp')^2 = 4\wp^3 - b, b \neq 0 \] and \[ a = (1 - m^2)/4, m \geq 2, m \neq 6n. \] They show under these conditions that all solutions to the Riccati differential equation are meromorphic and provide a full investigation of their periodicity and double periodicity.
Mathematics Subject Classification ID: 34M05
Mathematics Subject Classification ID: 34M10
Mathematics Subject Classification ID: 34C25
zbMATH DE Number: 1498578
zbMATH Keywords: Riccati differential equation
reviewed by: Mykola Grygorenko
MaRDI profile type: Publication
cites work: Meromorphic solutions of the Riccati differential equation
cites work: Q3037791
cites work: On a theorem of Picard
cites work: Q4001253
cites work: Q3982405
cites work: Nevanlinna theory and complex differential equations
full work available at URL: https://doi.org/10.1007/bf03322431
OpenAlex ID: W2156357644
description: scientific article; zbMATH DE number 1498578