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In this article, we investigate the existence and multiplicity of solutions of Kirchhoff equation \begin{equation*} \left{ \begin{aligned} -(1+b \int_{^3}|\nabla u|^2)\Delta u= k(x)\frac{|u|^2 u}{|x|} +\lambda h(x)u,~~x\in^3\ u(x)\rightarrow 0
\end{equation*} where the potential $k(x)$ allows sign changing. Making use of
Nehari manifold method and Concentration-compactness principle, we obtain the
existence and multiplicity of solutions for this equation.

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