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We consider a sequence of blow-up solutions to the Liouville-Gel’fand problem with variable coe‰cients, and their linearized eigenvalue problems. We show the precise coincidence of the Morse indices of the solution and the critical point of the Hamiltonian of the singular limit. The results are natural extensions of those for constant coe‰cients.

Morse Indices of the Solutions to the Liouville-Gel'fand Problem with Variable Coefficients