UAlberta-PIMS Mathematics and Statistics Colloquium: Pei-Yong Wang

This talk will cover the existence of a third solution through the Mountain Pass Lemma when the boundary data of the problem decreases below a threshold value. Meanwhile, an evolutionary perspective of the stability-instability of a solution of the stationary problem is gained through a parabolic comparison principle. This is necessary in examining the stability due to the lack of a comparison principle for the elliptic equation. Technically, the proof for the p-Laplacian is much more involved than for the case of Laplacian.