Multiple solutions for inhomogeneous elliptic problems involving critical Sobolev-Hardy exponents

Let Ω⊂RN be a smooth bounded domain such that 0∈Ω, N⩾3, 0⩽s<2, 2*(s):=2(N-s)/N-2 is the critical Sobolev-Hardy exponent, f(x) is a given function. By using the Ekeland's variational principle and the mountain pass lemma, we prove the existence of multiple solutions for the singular critical inhomogeneous problem-Δu-μu|x|2=|u|2*(s)-2|x|su+λu+f(x)with Dirichlet boundary condition on ∂Ω under some assumptions on f(x), λ and μ.