Abstract and Applied Analysis
Volume 2013 (2013), Article ID 568245, 11 pages
http://dx.doi.org/10.1155/2013/568245
Research Article

Existence of Conformal Metrics with Prescribed Q-Curvature

Mohammed Ali Al-Ghamdi,1 Hichem Chtioui,1 and Afef Rigane2

1Department of Mathematics, King Abdulaziz University, P.O. Box 80230, Jeddah, Saudi Arabia
2Department of Mathematics, Faculty of Sciences of Sfax, Road Soukra, Sfax, Tunisia

Received 13 October 2012; Revised 5 February 2013; Accepted 8 February 2013

Academic Editor: Svatoslav Staněk

Copyright © 2013 Mohammed Ali Al-Ghamdi et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We consider the problem of existence of conformal metrics with prescribed Q-curvature on standard sphere . Under the assumption that the order of flatness at critical points of prescribed Q-curvature function is , we give precise estimates on the losses of the compactness, and we prove new existence and multiplicity results through an Euler-Hopf type formula.