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Information Center for Mathematical Science

논문검색

Information Center for Mathematical Science

논문검색

Tohoku Mathematical Journal. Second Series
( Vol. 55 NO.1 / (2003))
Riccati Differential Equations with Elliptic Coefficients II
Katsuya Ishizaki, Ilpo Laine, Shun Shimomura, Kazuya Tohge,
Pages. 99-108
Abstract We study a Riccati differential equation whose coefficient is expressible in
terms of a special Weierstrass pe-function. We show that all the solutions are meromorphic,
and examine the periodicity of them.
Contents 1. Introduction
2. Properties of the elliptic function $\wp_0(z)$
3. Proofs of theorems 1.1 and 1.2
4. Proof of theorem 1.3
Key words Meromorphic function, Riccati equation, Weierstrass $\wp$ function
Mathmatical Subject Classification 34M05, 34A34