A multiplicity result for the problem $δd ξ= f'(<ξ,ξ>)ξ$

Details A multiplicity result for the problem $δd ξ= f'(<ξ,ξ>)ξ$ A multiplicity result for the problem $δd ξ= f'(<ξ,ξ>)ξ$

2007-01-25

arxiv.org/abs/math/0701757v1

Mathematics

Analysis of PDEs

24 pages

Scientific paper

In this paper we consider the nonlinear equation involving differential forms on a compact Riemannian manifold $\delta d \xi = f'(<\xi,\xi>)\xi$. 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. $f'(t)\geq\epsilon>0$ uniformly) and in the zero mass case ($f'(t)\geq 0$ and $f'(0)=0$) where a strong convexity hypothesis on the nonlinearity is assumed.

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