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

2001/01/11 by Zindine Djadli, Djadli, Zindine, Andrea Malchiodi +3
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Nonlinear Differential Equations Analysis #Nonlinear Partial Differential Equations #math.AP #math.DG #msc:35B45 #msc:35J60 #msc:53A30 #msc:53C21 #msc:58G30

paper · pdf · doi:10.48550/arxiv.math/0101101

27 pages

arxiv created 2001/01/11 · arxiv updated 2009/11/30

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.

Citations

• A relation between pointwise convergence of functions and convergence of functionals

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