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Admissible solutions of the Schwarzian differential equation. (English) Zbl 0733.34009

This paper is a sequel of a previous paper by the same author and with the same title [Res. Rep. Tokyo Nat. College Tech. 20 (1988)]. In both papers the author considered the Schwarzian differential equation \((*)\quad \{w,z\}^ m=R(z,w),\) and showed that if (*) possesses an admissible solution, then \[ d+2m\sum^{\ell}_{j=1}\delta (\alpha_ j,w)\leq 4m, \] where R(z,w) is a rational function of w with meromorphic coefficients and \(\alpha_ j\) are distinct complex constants. The author investigated the case \(m=1\) and \(d\geq 0\) in his previous paper, while he considers the case \(m\geq 1\) and \(d\geq 0\) in the present paper.
Reviewer: F.M.Ragab (Cairo)

MSC:

34M99 Ordinary differential equations in the complex domain
34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
34D35 Stability of manifolds of solutions to ordinary differential equations
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