Critical points at infinity in a fourth order elliptic problem with limiting exponent Original Research Article

This paper is concerned with the following nonlinear elliptic problem (P)(P): Δ2u=uqΔ2u=uq, u>0u>0 in ΩΩ, Δu=u=0Δu=u=0 on ∂Ω∂Ω, where ΩΩ is a bounded smooth domain in RnRn, n⩾6n⩾6 and q+1=2n/(n-4)q+1=2n/(n-4) is the critical Sobolev exponent. We provide a version of Morse Lemma at infinity for this problem. As application, we characterize the critical points at infinity of the associated variational problem. We also compute the difference of the topology that these critical points at infinity induce between the level sets of the functional corresponding to the problem.