The supercritical Lane-Emden-Fowler equation in exterior domains

Juan Dávila
Universidad de Chile, CMM (UMI CNRS)
email: jdavila@dim.uchile.cl

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

where is a domain with smooth boundary in , and .

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

 (1)

 (2)

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

uniformly in , and all have the same slow decay at infinity:

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).