We study existence, multiplicity and qualitative properties of entire solutions for a noncompact problem related to second-order interpolation inequalities with weights. More precisely, we deal with the following family of equations
Δu=λ|x|^{-4}u+|x|^{-β}|u|^{q-2}u in R^N,
where N≥5, q>2, β=N-q(N-4)2 and λ∈R is smaller than the Rellich constant.
