Classification of positive singular solutions to a nonlinear biharmonic equation with critical exponent
Résumé
For n ≥ 5, we consider positive solutions u of the biharmonic equation Δ^2 u = u^[(n+4)/(n-4)] on R^n\{0} with a nonremovable singularity at the origin. We show that lxl^[(n-4)/2] u is a periodic function of ln IxI and we classify all periodic functions obtained in this way. This result is relevant for the description of the asymptotic behavior of local solutions near singularities and for the Q-curvature problem in conformal geometry.
Domaines
Mathématiques [math]
Origine : Fichiers produits par l'(les) auteur(s)