The effect of domain topology on the number of positive solutions for singular elliptic problems involving the Caffarelli-Kohn-Nirenberg inequalities

In this paper we consider the critical singular equation involving the Caffarelli-Kohn-Nirenberg inequalities of the type(P1){−div(|x|−2a∇u)−μu|x|2(1+a)=λ|u|q−2u|x|dD+|u|p−2u|x|bp,x∈Ω,u>0,x∈Ω,u=0,x∈∂Ω. Here Ω is a bounded domain with smooth boundary in RN and contains 0 in its interior, 0⩽μ<(μ¯−a)2, μ¯=(N−22)2, N⩾3, a⩽b