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: [Formula: see text] where [Formula: see text] , [Formula: see text] , [Formula: see text] , and [Formula: see text] are constants and [Formula: see text] is the Hardy–Sobolev exponent in [Formula: see text] . For a suitable function [Formula: see text] , we establish the existence of multiple solutions by using the Nehari manifold and fibering maps. Moreover, we regard [Formula: see text] as a parameter to obtain the convergence property of solutions for the given problem as [Formula: see text] by the mountain pass theorem and Ekeland’s variational principle.