| In this paper,we will use classical variational method to investigate the ex-istence of positive solutions for the following semilinear elliptic equation systems,which is involved with critical Sobolev exponent and has the type(?)where Ω is a bounded domain in RN(N≥4),K(x),Q(x),H(x)are positive continuous functions on Ω,1<α,β<2*-1 and α+β=2*,2*= 2N/N-2 is the Sobolev critical exponent.We proved that the equation systems exists positive solution when K(x),Q(x)y H(x)and α,β satisfied some conditions. |