A multiplicity result for the problem delta d xi = f '() xi

摘要

In this paper we consider the nonlinear equation involving differential forms on a compact Riemannian manifold delta d xi = f'() 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) >= epsilon > 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. (C) 2007 Elsevier Ltd. All rights reserved.