Positive versus compact support solutions to a singular elliptic problem

The semilinear elliptic problem−Δu=K(x)(−uq+λup),u⩾0inΩ,u=0,on∂Ω, is considered in this paper, where Ω   is a bounded domain of RN(N⩾2)RN(N⩾2) with C2C2 boundary, 0