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Prescribing a fourth order conformal invariant on the standard sphere. I: A perturbation result. (English) Zbl 1023.58020
The authors study some fourth-order elliptic equations involving the critical Sobolev exponent, related to the prescription of a fourth order conformal invariant on the standard sphere. It is used a topological method to prove the existence of at least one solution when the function to be prescribed is close to a constant and a finite dimensional map associated to it has non-zero degree.
MSC:
58J60Relations of PDE with special manifold structures
35B40Asymptotic behavior of solutions of PDE
58J05Elliptic equations on manifolds, general theory