Asymptotic behavior of the unique solution for a fractional Kirchhoff problem with singularity

In this paper, we consider the following fractional Kirchhoff problem with singularity [Please download the PDF to view the mathematical expression], where [(-[DELTA]).sup.s] is the fractional Laplacian with 0 < s < 1, b [greater than or equal to] 0 is a constant and 0 < [gamma] < 1. Under certain assumptions on V and f, we show the existence and uniqueness of positive solution [u.sub.b] by using variational method. We also give a convergence property of [u.sub.b] as b [right arrow] 0, where b is regarded as a positive parameter. Keywords: fractional Kirchhoff problem; singularity; uniqueness; variational method; asymptotic behavior