CONCENTRATION PHENOMENA FOR FOURTH-ORDER ELLIPTIC EQUATIONS WITH CRITICAL EXPONENT

We consider the nonlinear equation [GRAPHICS] with u > 0 in Omega and u = Delta u = 0 on partial derivative Omega. Where Omega is a smooth bounded domain in R-n, n >= 9, and epsilon is a small positive parameter. We study the existence of solutions which concentrate around one or two points of Omega. We show that this problem has no solutions that concentrate around a point of Omega as epsilon approaches 0. In contrast to this, we construct a domain for which there exists a family of solutions which blow-up and concentrate in two different points of Omega as epsilon approaches 0.