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.
Mots-clés : 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}, pages = {259--295}, publisher = {Annales math\'ematiques Blaise Pascal}, volume = {12}, number = {2}, year = {2005}, doi = {10.5802/ambp.207}, zbl = {05016092}, language = {en}, url = {http://www.numdam.org/articles/10.5802/ambp.207/} }
TY - JOUR AU - El Mehdi, Khalil TI - Prescribing $Q$-curvature on higher dimensional spheres JO - Annales mathématiques Blaise Pascal PY - 2005 SP - 259 EP - 295 VL - 12 IS - 2 PB - Annales mathématiques Blaise Pascal UR - http://www.numdam.org/articles/10.5802/ambp.207/ DO - 10.5802/ambp.207 LA - en ID - AMBP_2005__12_2_259_0 ER -
%0 Journal Article %A El Mehdi, Khalil %T Prescribing $Q$-curvature on higher dimensional spheres %J Annales mathématiques Blaise Pascal %D 2005 %P 259-295 %V 12 %N 2 %I Annales mathématiques Blaise Pascal %U http://www.numdam.org/articles/10.5802/ambp.207/ %R 10.5802/ambp.207 %G en %F AMBP_2005__12_2_259_0
El Mehdi, Khalil. Prescribing $Q$-curvature on higher dimensional spheres. Annales mathématiques Blaise Pascal, Tome 12 (2005) no. 2, pp. 259-295. doi : 10.5802/ambp.207. http://www.numdam.org/articles/10.5802/ambp.207/
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