Positive solutions for nonhomogeneous elliptic equations involving critical Sobolev exponent

In this paper, we study the existence and multiplicity of positive solutions for the Dirichlet problem −Δu=λf(z)|u|q−2u+g(z)|u|2∗−2u in Ω, where λ>0λ>0,1≤q<21≤q<2,2∗=2N/(N−2)2∗=2N/(N−2),0∈Ω⊂RN(N≥3)0∈Ω⊂RN(N≥3) is a bounded domain with smooth boundary ∂Ω∂Ω, and ff,gg are nonnegative continuous functions on Ω¯.