A multiplicity result for the problem δdξ=f′(〈ξ,ξ〉)ξ

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>0f′(t)≥ε>0 uniformly) and in the zero mass case (f′(t)≥0f′(t)≥0 and f′(0)=0f′(0)=0) where a strong convexity hypothesis on the nonlinearity is assumed.