Abstract

We consider the problem: - ?u = |u|N-2/4 u + ef(x) in O, u = 0 on ?O, where O ? RN is a bounded smooth domain which exhibits small holes, f = 0, f ? 0 and e > 0 is small. Using the reduction method and a min-max scheme worked out with topological arguments, we construct multiple solutions by gluing negative double-spike patterns located near each of the holes.