Tuen-Wai Ng, HKU, Hong Kong

Two-variable Wiman-Valiron theory and its applications to PDEs



The classical Wiman-Valiron theory is an important tool for the study of entire solutions of ODEs in the complex plane. A two variable version of Wiman-Valiron theory was developed by Peter Fenton in 1995 and it has been applied to study the entire solutions of some PDEs by Peter Fenton and John Rossi very recently. In this talk, we shall explain how their techniques can be used to show that certain PDEs cannot have transcendental entire solutions.