Existence and concentration of solutions with compact support for elliptic problems with critical growth in RN

For a continuous and sign-changing function a(x), we study the existence and asymptotic behavior of compactly supported solutions of the following elliptic problem in RN with N⩾3:−Δu=aγ(x)uq+up,u⩾0 and u∈D1,2(RN), where γ>0, 0