A multiplicity result for the problem $δd ξ= f&#39;(<ξ,ξ>)ξ$

Abstract

In this paper we consider the nonlinear equation involving differential forms on a compact Riemannian manifold $δd ξ= f&#39;(<ξ,ξ>)ξ$. 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. $f&#39;(t)\geqε>0$ uniformly) and in the zero mass case ($f&#39;(t)\geq 0$ and $f&#39;(0)=0$) where a strong convexity hypothesis on the nonlinearity is assumed.