PRESCRIBING A FOURTH ORDER CONFORMAL INVARIANT ON THE STANDARD SPHERE — PART I: A PERTURBATION RESULT

Author:

DJADLI ZINDINE1,MALCHIODI ANDREA2,AHMEDOU MOHAMEDEN OULD3

Affiliation:

1. Université de Cergy-Pontoise, Département de Mathématiques, Site de Saint-Martin, 2 Avenue Adolphe Chauvin, F 95302 Cergy-Pontoise Cedex, France

2. School of Mathematics, Institute for Advanced Study, 1 Einstein Drive, Princeton, New Jersey, 08540, USA

3. Rheinische Friedrich-Wilhelms- Universitat Bonn, Matematische Institut, Beringstrasse 4, D 53115 Bonn, Germany

Abstract

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

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,General Mathematics

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