Positive solutions of a fourth-order semilinear problem involving critical growth

Abstract

Abstract In this work we study the existence of positive solutions of the critical problem (P) ∆2u+ a(x)u = |u|2**-2u, ℝN and u ∈ D2,2 (ℝN), where 2** = 2N/(N - 4), N ≥ 5, a ∈ LN/4 (ℝN) is on a nonnegative continuous function and ∆2 is the biharmonic operator. We also prove a global compactness result for the associated energy functional of problem (P), similar to that due to Struwe in [22]. The basic tool employed here is the concentration compactness due to P. L. Lions and a linking theorem on the cone of nonnegative functions.