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
Andrea Malchiodi. "Morse theory and a scalar field equation on compact surfaces." Adv. Differential Equations 13 (11-12) 1109 - 1129, 2008. https://doi.org/10.57262/ade/1355867288
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