The classifications of differential equations and the Painlevé transcendental functions
Speaker:Prof. Wenjun Yuan
Department of Applied Mathematics
Guangzhou University
Date & Time:18 Jan 2013 (Friday) 10:30
Venue:JM12
Organized by:Department of Mathematics

Abstract

In this talk, we will introduce some basic concepts and results about the special functions, which often arise as solutions of differential equations. One of the most useful classes of special functions are the Painlevé transcendent. They are defined by second order ordinary differential equations whose singularities have the Painlevé property: the only movable singularities are poles. This property is shared by all linear ordinary differential equations but is rare in nonlinear equations. Poincaré and L. Fuchs showed that any first order equation with the Painlevé property can be transformed into the Weierstrass equation or the Riccati equation, which can all be solved explicitly in terms of integration and previously known special functions.

Biography

Prof. Wenjun Yuan is currently a Professor of Department of Applied Mathematics at Guangzhou University. Prof. Yuan obtained his Ph.D. in Institute of Mathematics in Academia Sinica. The publication of Prof. Yuan include, Growth of entire solutions of algebraic differential equations, Further results of the estimate of growth of entire solutions of some classes of algebraic differential equations, A note on normal families of meromorphic functions and sharing set, On the estimate of growth of entire solutions of some classes of algebraic differential equations, and Normal criteria of function families concerning shared values etc.