In this paper, we are concerned with the following class of elliptic problems:where 2 = 2N/（N-2） is the critical Sobolev exponent, 2 < q < 2 , 0≤μ < μˉ=（N-2）24 , a（x）, k（x） ∈ C（RN ）. Through a compactness analysis of the functional corresponding to the problems , we obtain the existence of positive solutions for this problem under certain assumptions on a（x） and k（x）.
