We consider a scalar field equation on compact surfaces which has variational structure. When the surface is a torus and a physical parameter ρ belongs to $(8\pi, 4\pi^2 )$ we show under some extra assumptions that, as conjectured in [9], the functional admits at least three saddle points other than a local minimum.

1 aDe Marchis, Francesca uhttps://www.math.sissa.it/publication/multiplicity-solutions-mean-field-equation-compact-surfaces