Asymptotic behavior of least energy solutions of a biharmonic equation in dimension four

In this paper we consider a biharmonic equation on a bounded domain in R-4 with large exponent in the nonlinear term. We study asymptotic behavior of positive solutions obtained by minimizing suitable functionals. Among other results, we prove that c(p), the minimum of energy functional with the nonlinear exponent equal to p, is like rho(4)e / p as p -> +infinity, where rho(4) = 32 omega(4) and omega(4) is the area of the unit sphere S-3 in R4. Using this result, we compute the limit of the L-infinity-norm of least energy solutions as p -> + infinity. We also show that such solutions blow up at exactly one point which is a critical point of the Robin function.