The structure of the solution set for a mean field equation
Hiroshi Ohtsuka · EPrints - Department of Mathematics, Hokkaido University · 2007
The equation like (1) is sometimes called a mean field equation because it appears in the mean field limit of the equilibrium states for the vortex system of one species [5, 6, 15], see also general references of this field [21, 18, 23]. Associating −λ and v/λ with the inverse temperature of the state and the Hamiltonian of the system, we are able to see that the non-linear term of (1) resembles the canonical Gibbs measure as follows: e ∫ M edvg = e−(−λ) v λ ∫