The paper presents an analysis of multi-peak solutions of the following singularly perturbed problem
where is a smooth domain in ( does not have to be bounded) and is small parameter; the term is a superlinear, subcritical nonlinearity. The analysis is based on a variational method. By modifying the nonlinearity and adding a penalization term the authors introduce a new penalized energy functional and analyze its critical points. Section 1 of the paper includes the analysis of a single peak case and Section 2 treats the general multi-peak case.