PDE seminar Bifurcation branch of positive solution to semilinear elliptic equation with harmonic potential

Date
2010-10-4 16:30 - 2010-10-4 17:30
Place
Faculty of Science Building #3 Room 202
Speaker/Organizer
Hiroaki Kikuchi (Hokkaido University)
 
In this talk, we consider the existence and the non-existence of positive solution
to semilinear elliptic equation with harmonic potential and pure power nonlinearity.
It is proved by Hirose and Ohta ('02, '07) that the positive solution exists
uniquely for the Sobolev subcritical nonlinearity.
However, numerical computation suggests that the situation drastically changes for
the Sobolev critical and supercritical nonlinearity.
I will explain it more precisely and present some related results.
This is a joint work with Fouad Hadj Selem (Reims Univ.)