Conformal metrics with prescribed Q-curvature on S

Bensouf, Aymen; Chtioui, Hichem
July 2011
Calculus of Variations & Partial Differential Equations;Jul2011, Vol. 41 Issue 3/4, p455
Academic Journal
In this paper we prescribe a fourth order conformal invariant on the standard n-sphere, with n ≥ 5, and study the related fourth order elliptic equation. We prove new existence results based on a new type of Euler-Hopf type formula. Our argument gives an upper bound on the Morse index of the obtained solution. We also give a lower bound on the number of conformal metrics having the same Q-curvature.


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