Entire solutions for a class of elliptic equations involving p-biharmonic operator and Rellich potentials

We study existence, multiplicity and qualitative properties of entire solutions for a noncompact problem related to p-biharmonic type equations with weights. More precisely, we deal with the following family of equationsΔp2u=λ|x|−2p|u|p−2u+|x|−β|u|q−2uin RN, where N>2p, p>1, q>p, β=N−qp(N−2p) and λ∈R is smaller than the Rellich constant.