Multi-peak solutions for a wide class of singular perturbation problems

This paper concerns a wide class of singular perturbation problems arising from such diverse fields as phase transitions, chemotaxis, pattern formatio n, population dynamics and chemical reaction theory. The corresponding elli ptic equations in a bounded domain without any symmetry assumptions are stu died. It is assumed that the mean curvature of the boundary has (M) over ba r isolated, non-degenerate critical points. Then it is shown that for any p ositive integer M less than or equal to (M) over bar there exists a station ary solution with M local peaks which are attained on the boundary and whic h lie close to these critical points. The method is based on Lyapunov-Schmi dt reduction.