ASYMPTOTIC BEHAVIOR AND EXISTENCE RESULTS FOR A BIHARMONIC EQUATION INVOLVING THE CRITICAL SOBOLEV EXPONENT IN A FIVE-DIMENSIONAL DOMAIN

In this paper, we consider the problem (Q(epsilon)) : Delta(2)u = u(9) + epsilon f(x) in Omega, u = Delta u = 0 on partial derivative Omega, where Omega is a bounded and smooth domain in R-5, epsilon is a small positive parameter, and f is a smooth function. Our main purpose is to characterize the solutions with some assumptions on the energy. We prove that these solutions blow up at a critical point of a function depending on f and the regular part of the Green's function. Moreover, we construct families of solutions of (Q(epsilon)) which satisfy the conclusions of the first part.