Abstract: Let Ω be a smooth bounded domain such that 0∈Ω, N≥5, 2*:=(2N)/(N-4) is the critical Sobolev exponent, and f(x) is a given function. By using the variational methods, the paper proves the existence of solutions for the singular critical in the homogeneous problem Δ^u-μu/(|x|4)=|u|^2*-2u+f(x) with Dirichlet boundary condition on Ω under some assumptions on f(x) and μ.

Key words: biharmonic ,  equation; ,  critical ,  Sobolev ,  exponents; ,  compactness; ,  variational
methods