Meromorphic solutions of higher order Briot–Bouquet differential equations

Meromorphic solutions of higher order Briot–Bouquet differential equations

For differential equations P(y(k), y)=0, where P is a polynomial, we prove that all meromorphic solutions having at least one pole are elliptic functions, possibly degenerate.

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Veröffentlicht in:Mathematical proceedings of the Cambridge Philosophical Society 2009-01, Vol.146 (1), p.197-206
Hauptverfasser: EREMENKO, ALEXANDRE E, LIAO, LIANGWEN, NG, TUEN WAI
Format: Artikel
Sprache:eng
Schlagworte:
Differential equations
Mathematics
Polynomials
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Zusammenfassung:For differential equations P(y(k), y)=0, where P is a polynomial, we prove that all meromorphic solutions having at least one pole are elliptic functions, possibly degenerate.
ISSN:0305-0041
1469-8064
DOI:10.1017/S030500410800176X