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Information Center for Mathematical Science

논문검색

Information Center for Mathematical Science

논문검색

Kodai Mathematical Journal
( Vol. 20 NO.2 / (1997))
On the Schwarzian Differential Equation $\{w, z\} = R(z, w)$
Katsuya Ishizaki,
Pages. 67-78
Abstract It is showed in this note that if the Schwarzian differential equation
$(ast) {w, z} = R(z, w) = P(z, w)/Q(z, w),$ where $P(z, w)$ and $Q(z, w)$
are polynomials in $w$ with meromorphic coefficients, possesses an admissible
solution $w(z),$ then $w(z)$ satisfies a first order equation of the form
$(ast ast) (w')^2 + B(z, w)w' + A(z, w) = 0,$ where $B(z, w)$ and $A(z, w)$,
are polynomials in $w$ having small coefficients with respect to $w (z),$ or by
a suitable Mobius transformation $(ast)$ reduces into ${w, z} = P(z, w)/(w +
b(z))^2$ or ${w, z} = c(z).$ Furthermore, we study the equation $(ast
ast).$
Contents 1. Introduction
2. Preliminary Lemmas
3. Proof of Theorem 1.1
4. Proof of Theorem 1.2
Key words
Mathmatical Subject Classification