SMS scnews item created by Daniel Daners at Fri 7 Sep 2012 0900
Type: Seminar
Modified: Fri 7 Sep 2012 1002
Distribution: World
Expiry: 10 Sep 2012
Calendar1: 10 Sep 2012 1400-1500
CalLoc1: AGR Carslaw 829
Auth: daners@bari.maths.usyd.edu.au

# On a perturbed q-curvature problem in S4

### Santra

Sanjiban Santra
University of Sydney
10rd September 2012 2-3pm, AGR Carslaw 829

## Abstract

Let $$g_0$$ denote the standard metric on $$\mathbb S ^4$$ and let $$P_{g_0}:=\Delta^2_{g_{0}}-2\Delta_{g_{0}}$$ denote the corresponding Paneitz operator. In this work, we study the fourth order elliptic problem with exponential nonlinearity $P_{g_{0}} u + 6 = 2Q(x)e^{4u}$ on $$\mathbb{S}^4$$. Here $$Q$$ is a prescribed smooth function on $$\mathbb{S}^4$$ which is assumed to be a perturbation of a constant. We prove existence results to the above problem under assumptions only on the shape'' of $$Q$$ near its critical points. These are more general than the non-degeneracy conditions assumed so far. We also show local uniqueness and exact multiplicity results for this problem. The main tool used is the Lyapunov-Schmidt reduction.

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

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