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)


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