Abstract. In this talk, I will present some results on the number, location and non-degeneracy of critical points of the Robin functions in bounded domains with small holes. Such results play an important role in the study of bubbling/peak solutions for well-studied nonlinear elliptic problems. his is a joint work with Gladiali, Grossi and Peng Luo.

Bio: Shusen Yan is a professor in the School of Mathematics and Statistics, Central China Normal University. He obtained his PhD in 1990 from the Institute of System Science, Chinese Academy of Science. His research interest is in nonlinear elliptic partial differential equations. In the last two decades, he mainly works on the existence, the non-degeneracy and the local uniqueness of peak/bubbling solutions for nonlinear elliptic problems and successfully solves some important problems such as the estimates of the number of solutions for Ambrosetti-Prodi type elliptic problems which were raised in 1980s by Lazer and McKenna; the existence of infinitely many positive solutions for some non-compact elliptic problems, the exact number of solutions for Chern-Simons equations.