Let be a smooth bounded domain in , . This paper deals with 2-peak solutions of the Dirichlet problem:
with for , for . Let be the unique positive solution in of , at , . Consider the energy functional
and set . Denote by [resp. the set of such that [resp. ], where is small enough.
The authors use methods and results in algebraic topology to study the contribution to the relative homology of 2-peak solutions of (1), as . They also obtain informations on the existence of a 2-peak solution and on the locations of the two peaks.