Problem with critical Sobolev exponent and with weight

Rejeb Hadiji (1) , Habib Yazidi

1 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées

The authors consider the problem: -div(p del u) = u(q-1) + lambda u, u > 0 in Omega, u = 0 on partial derivative Omega, where Omega is a bounded domain in R-n, n >= 3, p : (Omega) over bar -> R is a given positive weight such that p epsilon H-1(Omega) boolean AND C((Omega) over bar, lambda is a real constant and q = 2n/n-2, and study the effect of the behavior of p near its minima and the impact of the geometry of domain on the existence of solutions for the above problem.

Domaines: Physique mathématique [math-ph]

Rejeb Hadiji, Habib Yazidi. Problem with critical Sobolev exponent and with weight. Chinese Annals of Mathematics - Series B, 2007, 28 (3), pp.327--352. ⟨10.1007/s11401-005-0435-y⟩. ⟨hal-00693089⟩