Existence of Positive Solutions for a Class of Almost Critical Problems on an Annulus

Abstract. In this paper we will consider multipeak positive solutions for a class of slightly subcritical or slightly supercritical elliptic problems on an annulus with Dirichlet boundary conditions. By using the explicit form of the Green function and of the Robin function on the annulus, we prove that the annulus becomes thinner and thinner as the number of bumps increases for the slightly subcritical case, while the hole of the annulus is very small for the slightly supercritical case.