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Meromorphic solutions of some complex differential equations. (English) Zbl 1072.34514

Kiselman, Christer (ed.), Complex analysis and differential equations. Proceedings of the Marcus Wallenberg symposium in honor of Matts Essén, Uppsala, Sweden, June 15–18, 1997. Uppsala: Uppsala University (ISBN 91-554-4495-4/pbk). Acta Univ. Ups. Skr. Upps. Univ. C Organ. Hist. 64, 187-193 (1999).
From the text: For the differential equation \((*) y^nP[y] + b y^m P[y] + c = 0\), where \(P[y]\not\equiv0\) is a differential polynomial in \(y\), \(m\) and \(n\) are distinct nonnegative integers, \(n\geq1\), and \(b\) and \(c\) are meromorphic functions in the plane, the authors prove the following theorem: Equation \((*)\) possesses no meromorphic solution \(f\) satisfying \(T(r, b) = S(r,f)\) and \(T(r, c) = S(r,f)\).
For the entire collection see [Zbl 0936.00055].

MSC:

34M05 Entire and meromorphic solutions to ordinary differential equations in the complex domain
30D35 Value distribution of meromorphic functions of one complex variable, Nevanlinna theory
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