We consider a scalar field equation on compact surfaces which have variational structure. When the surface is a torus and a physical parameter \rho belongs to (8\pi,4\pi^2), we show under some extra assumptions that, as conjectured in [De Marchis, Comm. PDE 2008], the functional admits at least three saddle points other than a local minimum.
Multiplicity of solutions for a mean field equation on compact surfaces / DE MARCHIS, Francesca. - In: BOLLETTINO DELLA UNIONE MATEMATICA ITALIANA. - ISSN 1972-6724. - STAMPA. - 4:9(2011), pp. 245-257.
Multiplicity of solutions for a mean field equation on compact surfaces
DE MARCHIS, FRANCESCA
2011
Abstract
We consider a scalar field equation on compact surfaces which have variational structure. When the surface is a torus and a physical parameter \rho belongs to (8\pi,4\pi^2), we show under some extra assumptions that, as conjectured in [De Marchis, Comm. PDE 2008], the functional admits at least three saddle points other than a local minimum.File allegati a questo prodotto
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