Abstract
In this paper we consider the following biharmonic equation with critical exponent (P-epsilon): Delta(2) u = Ku n+4/n-4-epsilon, u > 0 in Omega and u =Delta u = 0 on partial derivative Omega, where Omega is a smooth bounded domain in R-n, n >= 5, epsilon is a small positive parameter, and K is a smooth positive function in (Omega) over bar. We construct solutions of (P-epsilon) which blow up and concentrate at strict local maximum of K either at the boundary or in the interior of Omega. We also construct solutions of ( P-epsilon) concentrating at an interior strict local minimum point of K. Finally, we prove a nonexistence result for the corresponding supercritical problem which is in sharp contrast to what happened for (P-epsilon).