Abstract
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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