A multiplicity result for the problem $\delta d\xi =f^{\prime }(<\xi ,\xi >)\xi$

Abstract

In this paper we consider the nonlinear equation involving differential forms on a compact Riemannian manifold $\delta d\xi =f^{\prime }(<\xi ,\xi >)\xi$. 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. $f^{\prime }(t)\ge \epsilon >0$ uniformly) and in the zero mass case ($f^{\prime }(t)\ge 0$ and $f^{\prime }(0)=0$) where a strong convexity hypothesis on the nonlinearity is assumed.

24 pages