Prescribing a fourth order conformal invariant on the standard sphere - Part I: a perturbation result

Mathematics – Analysis of PDEs

Scientific paper

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27 pages

Scientific paper

In this paper we study some fourth order elliptic equation involving the critical Sobolev exponent, related to the prescription of a fourth order conformal invariant on the standard sphere. We use a topological method to prove the existence of at least a solution when the function to be prescribed is close to a constant and a finite dimensional map associated to it has non-zero degree.

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