Morse indices of multiple blow-up solutions to the two-dimensional Gel'fand problem

2012/10/04 by Gladiali, Francesca, Grossi, Massimo, Ohtsuka, Hiroshi +1 · 2 citations
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1210.1373

Abstract

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.

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• Qualitative properties of blowing-up solutions of nonlinear elliptic equations with critical Sobolev exponent
• Qualitative properties of single blow-up solutions for nonlinear Hartree equation with slightly subcritical exponent

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