Painlev'e di erential equations in the complex plane

By V. Gromak, I. Laine, S. Shimomura. 2002

326 citations recorded by the source corpus.

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Finite‐order meromorphic solutions and the discrete Painlevé equations (2005, result): “During the twentieth century it was confirmed by different authors (and by different methods) that these equations indeed possess the Painlevé property [31, 28, 27, 24, 17].”
Painlevé equations: nonlinear special functions (2003, background): “(ii) Bäcklund transformations and exact solutions of Painlevé equations; a summary of many of the currently known results is given in [87].”
On the Nevanlinna characteristic of f(z+η) and difference equations in the complex plane (2006, background): “We mention that the prime integrable difference equations are the discrete Painlevé equations which can be obtained from the classical Painlevé differential equations [12] via suitable discretizations.”
A Difference Picard Theorem for Meromorphic Functions of Several Variables (2009, methodology): “This lemma has also been used as an important tool in the study of value distribution of meromorphic solutions of differential equations in the complex plane [20, 23, 14].”