(untitled) (Analysis in Theory and Applications, 2022)
In this paper we consider the Dirichlet problem where ρ is a small parameter and Ω is a C^2 bounded domain in R^2. In [1], the author proves the existence of a m-point blow-up solution u_ρ jointly with its asymptotic behaviour. We compute the Morse index of u_ρ in terms of the Morse index of the associated Hamilton function of this problem. In addition, we give an asymptotic estimate for the first 4m eigenvalues and eigenfunctions.