Morse indices of multiple blow-up solutions to the two-dimensional   Gel'fand problem
  Blow-up solutions to the two-dimensional Gel'fand problem are studied. It is known that the location of the blow-up points of these solutions is related to a Hamiltonian function involving the Green function of the domain. We show that this implies an equivalence between the Morse indices of the solutions and the associated critical points of the Hamiltonian. 
Francesca Gladiali, Massimo Grossi, Hiroshi Ohtsuka, Takashi Suzuki
math.AP