Four solutions of an inhomogeneous elliptic equation with critical exponent and singular term

In this paper, we prove the existence of four nontrivial solutions of a elliptic equation with a Hardy singularity and show that at least one of them is sign changing. Our results extend some previous works on the literature, as Tarantello(1993), Kang-Deng(2005) and Hirano-Shioji(2005)