Generic multiplicity for a scalar field equation on compact surfaces
type: Item
instance of: scholarly article
title: Generic multiplicity for a scalar field equation on compact surfaces
zbMATH Open document ID: 1211.58011
author: Francesca De Marchis
published in: Journal of Functional Analysis
publication date: 2010-09-10T00:00:00Z
review text: Let \((M,g)\) be a compact Riemannian surface without boundary. The authors prove generic multiplicity of solutions as in the cases when the Euler characteristic of \(M\) is nonpositive. They prove generic multiplicity of solutions for a scalar field equation on compact surfaces via Morse inequalities. In particular, their result improves significantly the multiplicity estimate which can be deduced from the degree-counting formula by \textit{C.-C. Chen} and \textit{C.-S. Lin} [Commun. Pure Appl. Math. 56, No.~12, 1667--1727 (2003; Zbl 1032.58010)]. Moreover, related results are derived for the prescribed \(Q\)-curvature equation.
Mathematics Subject Classification ID: 58J05
Mathematics Subject Classification ID: 82B99
zbMATH DE Number: 5782198
zbMATH Keywords: geometric PDE's
zbMATH Keywords: generic multiplicity
zbMATH Keywords: Morse inequalities
zbMATH Keywords: scalar field equations
MaRDI profile type: Publication
full work available at URL: j.jfa.2010.07.003
OpenAlex ID: W2051818166
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DOI: 10.1016/J.JFA.2010.07.003
description: scientific article; zbMATH DE number 5782198