Abstract
We consider a biharmonic equation under the Navier boundary condition and with a nearly critical exponent (P epsilon): Delta(2)u = u(9-epsilon), u > 0 in Omega and u = Delta u = 0 on. theta Omega, where Omega is a smooth bounded domain in R-5, epsilon > 0. We study the asymptotic behavior of solutions of ( Pe) which are minimizing for the Sobolev quotient as e goes to zero. We show that such solutions concentrate around a point x(0)is an element of Omega as epsilon -> 0, moreover x(0) is a critical point of the Robin's function. Conversely, we show that for any nondegenerate critical point x(0) of the Robin's function, there exist solutions of (P epsilon) concentrating around x(0) as e -> 0. Copyright (c) 2006 Khalil El Mehdi.