Existence and multiplicity results for a fourth order mean field equation

In this article we consider the following fourth order mean field equation on smooth domain Omega subset of R-4. Delta(2)u = rho Ke(u)/integral(Omega)Ke(u) in Omega. u = Delta u = 0 on partial derivative Omega. where rho is an element of R and 0 < K is an element of C-2(Omega). Through a refined blow up analysis, we characterize the critical points at infinity of the associated variational problem and compute their contribution of the difference of topology between the level sets of the associated Euker-Lagrange funcitonal. We then use topological and dynamical methods to prove some existence and multiplicity results. (C) 2010 Elsevier Inc. All rights reserved.