Double-spike solutions for a critical inhomogeneous elliptic problem in domains with small holes

Abstract

In this paper we construct solutions which develop two negative spikes as epsilon -> 0(+) for the problem -Delta u = vertical bar u vertical bar(4/(N-2)) u + epsilon f(x) in Omega, u = 0 on partial derivative Omega, where Omega subset of R-N is a bounded smooth domain exhibiting a small hole, with f >= 0, f not equivalent to 0. This result extends a recent work of Clapp et al. in the sense that no symmetry assumptions on the domain are required.