Advances in Differential Equations
- Adv. Differential Equations
- Volume 13, Number 11-12 (2008), 1109-1129.
Morse theory and a scalar field equation on compact surfaces
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 . Employing these ingredients, we derive an alternative and direct proof (plus a clear interpretation) of a degree formula obtained in , which used refined blow-up estimates from  and . Related results are derived for the prescribed $Q$-curvature equation on four manifolds.
Adv. Differential Equations Volume 13, Number 11-12 (2008), 1109-1129.
First available in Project Euclid: 18 December 2012
Permanent link to this document
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 53C21: Methods of Riemannian geometry, including PDE methods; curvature restrictions [See also 58J60]
Secondary: 35B33: Critical exponents 35J60: Nonlinear elliptic equations 53A30: Conformal differential geometry
Malchiodi, Andrea. Morse theory and a scalar field equation on compact surfaces. Adv. Differential Equations 13 (2008), no. 11-12, 1109--1129. https://projecteuclid.org/euclid.ade/1355867288