Štvrtok 24.11.2011, 14:30-15:30, F1-326 / Thursday, November 24, 2011, 2:30-3:30 PM, F1-326

Eiji Yanagida (Tokyo Institute of Technology)

Exact multiplicity of rapidly decaying solutions for a semilinear elliptic equation with a critical exponent

Abstrakt/Abstract:

We consider the structure of radial solutions of a semilinear elliptic equation with the Sobolev critical exponent. It is shown that for every nonnegative integer $n$, there exists a weight function such that the equation has exactly $n$ rapidly decaying solutions. This result is proved in a constructive way by using a characterization of solutions in terms of the Pohozaev identity.