# American Institute of Mathematical Sciences

July  2010, 28(3): 875-897. doi: 10.3934/dcds.2010.28.875

## Hylomorphic solitons on lattices

 1 Dipartimento di Matematica Applicata "U. Dini”, Università di Pisa, via F. Buonarroti 1/c 56127 Pisa, Italy 2 Dipartimento di Matematica, Università di Bari and INFN sezione di Bari, Via Orabona 4, 70125 Bari, Italy

Received  March 2010 Revised  April 2010 Published  April 2010

This paper is devoted to the study of solitons whose existence is related to the ratio energy/charge. These solitons are called hylomorphic. In the first part of the paper we prove an abstract theorem on the existence of hylomorphic solitons which can be applied to the main situations considered in literature. In the second part, we apply this theorem to the nonlinear Schrödinger and Klein Gordon equations defined on a lattice.
Citation: Vieri Benci, Donato Fortunato. Hylomorphic solitons on lattices. Discrete & Continuous Dynamical Systems - A, 2010, 28 (3) : 875-897. doi: 10.3934/dcds.2010.28.875
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