Entire solutions for a class of variational problems involving the biharmonic operator and Rellich potentials

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 Δ2u=λ|x|−4u+|x|−β|u|q−2uin RN, where N≥5N≥5, q>2q>2, β=N−q(N−4)/2β=N−q(N−4)/2 and λ∈Rλ∈R is smaller than the Rellich constant.