Multiple existence of solutions for a semilinear elliptic problem with nonconstant coefficients

Let N⩾7,2*=2N/(N-2) and Ω⊂RN be a bounded domain with a smooth boundary ∂Ω and a:Ω¯⟶R is a continuous mapping. In this paper we consider the existence and multiplicity of positive solutions of Dirichlet boundary value problem of the form -▽(a(y)▽u)=|u|2*-2u,u∈H01(Ω).