The Nehari manifold and the existence of multiple solutions for a singular quasilinear elliptic equation

In this paper, we are concerned with the existence of multiple positive solutions for the singular quasilinear elliptic problem {−div(|x|−ap|∇u|p−2∇u)=λh(x)|u|m−2u+H(x)|u|n−2u,x∈Ω,u(x)=0,x∈∂Ω, where Ω⊂RN(N≥3) is a bounded domain with smooth boundary ∂Ω, 0∈Ω, 10. h(x),H(x) are Lebesgue measurable functions which may change sign on Ω. We prove that there exist at least two positive solutions by using the Nehari manifold and the fibrering maps associated with the energy functional for this problem.