摘要：In this paper, we consider the following fractional Kirchhoff problem with strong singularity: $$ \textstyle\begin{cases} (1 b\int _{\mathbb{R}^{3}}\int _{\mathbb{R}^{3}} \frac{ \vert u(x)-u(y) \vert ^{2}}{ \vert x-y \vert ^{3 2s}}\,\mathrm{d}x \,\mathrm{d}y )(-\Delta )^{s} u V(x)u = f(x)u^{-\gamma }, & x \in \mathbb{R}^{3}, \\ u>0,& x\in \mathbb{R}^{3}, \end{cases} $$ where $(-\Delta )^{s}$ is the fractional Laplacian with $00$ is a constant, and $\gamma >1$ . Since $\gamma >1$ , the energy functional is not well defined on the work space, which is quite different with the situation of $0<\gamma <1$ and can lead to some new difficulties. Under certain assumptions on V and f, we show the existence and uniqueness of a positive solution $u_{b}$ by using variational methods and the Nehari manifold method. We also give a convergence property of $u_{b}$ as $b\rightarrow 0$ , where b is regarded as a positive parameter.
