**SMS scnews item created by Daniel Daners at Wed 27 Aug 2014 1238**

Type: Seminar

Distribution: World

Expiry: 1 Sep 2014

**Calendar1: 1 Sep 2014 1400-1500**

**CalLoc1: AGR Carslaw 829**

Auth: daners@como.maths.usyd.edu.au

### PDE Seminar

# On a singular elliptic equation with a sign-changing nonlinearity

### Cirstea

Florica Cîrstea

The University of Sydney

1 Sep 2014, 2-3pm, Carslaw Room 829 (AGR)

## Abstract

Let $\Omega $ be an
open subset of ${\mathbb{R}}^{n}$
with $n\ge 3$ such
that $0\in \Omega $.
For $s\in \left(0,2\right)$ and
$q>1$ fixed, we consider
a positive function $u\in {C}^{\infty}\left(\Omega \backslash \left\{0\right\}\right)$
such that

$$-\Delta u=\frac{{u}^{{2}^{\star}\left(s\right)-1}}{|x{|}^{s}}-{u}^{q}\phantom{\rule{2em}{0ex}}\text{in}\Omega \backslash \left\{0\right\}\text{},$$ | (1) |

where ${2}^{\star}\left(s\right):=\frac{2\left(n-s\right)}{n-2}$
is critical from the viewpoint of the Hardy–Sobolev embeddings. In this talk, I
will present recent results on the classification of the behaviour near zero for the
positive solutions of (1).

This is joint work with Frédéric Robert (University of
Lorraine – Nancy).

Check also the PDE
Seminar page. Enquiries to Daniel Hauer or Daniel Daners.