Positive solutions for a nonlinear problem on a three-dimensional domain

Abstract

In this paper we provide a perturbation result for the following critical elliptic equation: –Δu = K(x)u5, u > 0 in Ω, u = 0, on ∂Ω, where Ω is a bounded domain of ℝ3. Our main assumption is that the function K satisfies a flatness condition near its critical points of order β greater than 1.