Multi-peak Solutions for a Singularly Perturbed Semilinear Elliptic Problem

This paper is concerned with the existence of multi-peak solutions of the following problem[formula] where Ω is a smooth bounded domain in N (N 2), >0 is a small positive number and p (2, ) for N 3, p (2, +∞) for N=2. Using a variational method we construct positive solutions concentrating near given “saddle points” of the distance function dist(•, ∂Ω). An explicit expression for the dominant parts of the solutions is also obtained.