Scalar curvature type problem on the three dimensional bounded domain

In this paper we prove an existence result for the nonlinear elliptic problem: Δu = K u5, u > 0 in Ω, u = 0 on ∂Ω, where Ω is a smooth bounded domain of ℝ3 and K is a positive function in Ω¯. Our method relies on studying its corresponding subcritical approximation problem and then using a topological argument.