Problem with critical Sobolev exponent and with weight
Abstract
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.