Asymptotic Behavior of Least Energy Solutions of a Biharmonic Equation in Dimension Four

Abstract. In this paper we consider a biharmonic equation on a bounded domain in R4 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 cp, the minimum of energy functional with the nonlinear exponent equal to p, is like ρ4e/p as p → +∞, where ρ4 = 32ω4 and ω4 is the area of the unit sphere S3 in R4. Using this result, we compute the limit of the L∞-norm of least energy solutions as p → +∞. We also show that such solutions blow up at exactly one point which is a critical point of the Robin function. 2000 Mathematics Subject Classification: 35J60, 35J65