Juan Dávila

Universidad de Chile, CMM (UMI CNRS)

email:`jdavila@dim.uchile.cl`

Universidad de Chile, CMM (UMI CNRS)

email:

**Abstract**: We consider the so called Lane-Emden-Fowler
equation,

We are interested in the case when is super-critical, i.e.
, and when the domain is an *exterior domain*, that is,
is of the form
where
be a
bounded open set with smooth boundary. Thus we
consider

The main result is that for any there is a continuum of solutions , small, to problem (1)-(2) such that

where .

This is joint work with Manuel del Pino (Universidad de Chile), Monica Musso (Politecnico di Torino & Universidad Católica) and Juncheng Wei (Chinese University of Hong Kong).