Some existence results for a fourth order equation involving critical exponent

In this paper a fourth order equation involving critical growth is considered under the Navier boundary condition: Δ2u = Kup, u > 0 in Ω, u = Δu = 0 on ∂Ω, where K is a positive function, Ω is a bounded smooth domain in Rn, n ≥ 5 and p + 1 2n/(n - 4) is the critical Sobolev exponent. We give some topological conditions on K to ensure the existence of solutions. Our methods involve the study of the critical points at infinity and their contribution to the topology of the level sets of the associated Euler Lagrange functional. (author)