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This paper is concerned with the following nonlinear Dirichlet problem:{-△pu =|u|p*- 2u + λf(x,u)x ∈Ω, u =0x ∈(e)Ω, where △pu=div(|(△)u|p-2(△)u) is the p-Laplacian of u,Ω is a bounded domain in Rn(n≥3),1 ＜ p ＜ n,p·=pn/n-p is the critical exponent for