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2008 Morse theory and a scalar field equation on compact surfaces
Andrea Malchiodi
Adv. Differential Equations 13(11-12): 1109-1129 (2008).

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.

Citation

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Andrea Malchiodi. "Morse theory and a scalar field equation on compact surfaces." Adv. Differential Equations 13 (11-12) 1109 - 1129, 2008.

Information

Published: 2008
First available in Project Euclid: 18 December 2012

zbMATH: 1175.53052
MathSciNet: MR2483132

Subjects:
Primary: 53C21
Secondary: 35B33, 35J60, 53A30

Rights: Copyright © 2008 Khayyam Publishing, Inc.

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Vol.13 • No. 11-12 • 2008
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