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Existence of Conformal Metrics with Prescribed Q‐Curvature

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  • Mohammed Ali Al-Ghamdi
  • Hichem Chtioui
  • Afef Rigane

Abstract

We consider the problem of existence of conformal metrics with prescribed Q‐curvature on standard sphere Sn, n ≥ 5. Under the assumption that the order of flatness at critical points of prescribed Q‐curvature function K(x) is β ∈ ]1, n − 4], we give precise estimates on the losses of the compactness, and we prove new existence and multiplicity results through an Euler‐Hopf type formula.

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Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:568245
DOI: 10.1155/2013/568245
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