### Morse theory and a scalar field equation on compact surfaces

Andrea Malchiodi

#### Abstract

The aim of this paper is to study a nonlinear scalar field equation on a surface $\Sigma$ via a Morse-theoretical approach, based on some of the methods in [25]. Employing these ingredients, we derive an alternative and direct proof (plus a clear interpretation) of a degree formula obtained in [18], which used refined blow-up estimates from [34] and [17]. Related results are derived for the prescribed $Q$-curvature equation on four manifolds.

#### Article information

Source
Adv. Differential Equations, Volume 13, Number 11-12 (2008), 1109-1129.

Dates
First available in Project Euclid: 18 December 2012