Yik-Man Chiang, HKUST, Hong Kong

Malmquist-type theorems for the Painleve equations

Abstract

Malmquist was able to classify first-order algebraic equations which admit at least one meromorphic solution. Variant of this idea has been applied to solve differential equations with meromorphic solutions in a number of recent works of Eremenko, Conte, Ng, etc. In this joint work with Halburd, we show that there are second order analogues for the Malmquist problem. This extends earlier work of Wittich and Ishisaki.