Localization of solutions for nonlinear elliptic problems with critical growth

Rejeb Hadiji (1) , Riccardo Molle (2) , Donato Passaseo (3) , Habib Yazidi (4)

1 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées
2 Dipartimento di Matematica [Rome]
3 Dipartimento di Matematica "E. De Giorgi",
4 ESSTT - Ecole Supérieure des Sciences et Techniques [Tunis]

We study the existence and the multiplicity of solutions for a problem with critical Sobolev exponent and with weight, when the set of the minimizers for the weight p has multiple connected component. We study also the case where this set has one connected component and has complex topology.

Domaines: Equations aux dérivées partielles [math.AP]

Rejeb Hadiji, Riccardo Molle, Donato Passaseo, Habib Yazidi. Localization of solutions for nonlinear elliptic problems with critical growth. C. R. Acad. Sci. Paris,, 2006, Ser. I (no 334), p. 725-730. ⟨hal-00795897⟩