Prescribing Q-curvature on higher dimensional spheres
Annales mathématiques Blaise Pascal, Volume 12 (2005) no. 2, p. 259-295

We study the problem of prescribing a fourth order conformal invariant on higher dimensional spheres. Particular attention is paid to the blow-up points, i.e. the critical points at infinity of the corresponding variational problem. Using topological tools and a careful analysis of the gradient flow lines in the neighborhood of such critical points at infinity, we prove some existence results.

DOI : https://doi.org/10.5802/ambp.207
Classification:  35J60,  53C21,  58J05
Keywords: Variational problems, lack of compactness, Q curvature, critical points at infinity
@article{AMBP_2005__12_2_259_0,
     author = {El Mehdi, Khalil},
     title = {Prescribing $Q$-curvature on higher dimensional spheres},
     journal = {Annales math\'ematiques Blaise Pascal},
     publisher = {Annales math\'ematiques Blaise Pascal},
     volume = {12},
     number = {2},
     year = {2005},
     pages = {259-295},
     doi = {10.5802/ambp.207},
     zbl = {05016092},
     language = {en},
     url = {http://www.numdam.org/item/AMBP_2005__12_2_259_0}
}
El Mehdi, Khalil. Prescribing $Q$-curvature on higher dimensional spheres. Annales mathématiques Blaise Pascal, Volume 12 (2005) no. 2, pp. 259-295. doi : 10.5802/ambp.207. http://www.numdam.org/item/AMBP_2005__12_2_259_0/

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