Multiplicity and asymptotic behavior of solutions for Kirchhoff type equations involving the Hardy-Sobolev exponent and singular nonlinearity

In this paper, we study a class of critical elliptic problems of Kirchhoff type: [a + b(∫R3|∇u|2-μ2/2 dx)2/2]( - Δu - μ2/) = 2/2 + λ2/,  where a, b > 0 , μ ∈ [0, 1/4) , α, β ∈ [0, 2) , and q ∈ (1, 2) are constants and 2∗(α) = 6 - 2α is the Hardy-Sobolev exponent in R3 . For a suitable function f(x) , we establish the existence of multiple solutions by using the Nehari manifold and fibering maps. Moreover, we regard b > 0 as a parameter to obtain the convergence property of solutions for the given problem as b ↘ 0+ by the mountain pass theorem and Ekeland's variational principle.