Ja n 20 07 A multiplicity result for the problem δdξ = f ′ ( 〈 ξ , ξ 〉
نویسنده
چکیده
In this paper we consider the nonlinear equation involving differential forms on a compact Riemannian manifold δdξ = f ′(〈ξ, ξ〉)ξ. This equation is a generalization of the semilinear Maxwell equations recently introduced in a paper by Benci and Fortunato. We obtain a multiplicity result both in the positive mass case (i.e. f ′(t) ≥ ε > 0 uniformly) and in the zero mass case (f ′(t) ≥ 0 and f ′(0) = 0) where a strong convexity hypothesis on the nonlinearity is assumed.
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