Multiple solutions for a class of Kirchhoff equation with singular nonlinearity

In this article, we investigate the existence and multiplicity of solutions of Kirchhoff equation \begin{equation*} \left\{ \begin{aligned} -(1+b \int_{\mathbb{R}^3}|\nabla u|^2)Δu= k(x)\frac{|u|^2 u}{|x|} +λh(x)u,~~x\in\mathbb{R}^3\\ u(x)\rightarrow 0 ~~~~~~~~~~~~~~~~~~~~~~~as ~~~~|x|\rightarrow\infty \end{aligned} \right. \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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