On a class of singular biharmonic problems involving critical exponents ✩

This paper deals with the following class of singular biharmonic problems (P) Δ2u + V (x)|u|q−1u = |u|2∗−2u, in Ω ⊂ RN, u ∈ D 2,2 o (Ω), N 5, where 1 q <2∗−1, 2∗ = 2N/(N −4) is the critical Sobolev exponent, Δ2 denotes the biharmonic operator, Ω is open domain (not necessarily bounded, it may be equal to RN) and V is a potential that changes sign in Ω with some points of singularities in Ω. Some results on the existence of solutions are obtained by combining the Mountain Pass Theorem and Hardy inequality with some arguments used by Brézis and Nirenberg.  2002 Elsevier Science (USA). All rights reserved.