Multiple positive solutions for a quasilinear elliptic equation involving singular potential and critical Sobolev exponent

In this paper, we are concerned with a class of quasilinear elliptic equation in which the potential is singular at the origin and the nonlinearity is pp-sublinear near the origin. By the Ekeland variational principle and Mountain Pass theorem, we prove that there exist at least two positive solutions under suitable assumptions on the potential and the nonlinearity.