Hylomorphic solitons on lattices

Vieri Benci; Donato Fortunato

doi:10.3934/dcds.2010.28.875

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2010, Volume 28, Issue 3: 875-897. Doi: 10.3934/dcds.2010.28.875

This issue Previous Article A Liouville theorem for solutions to the linearized Monge-Ampere equation Next Article Partial regularity for elliptic equations

Hylomorphic solitons on lattices

Vieri Benci^1, and
Donato Fortunato^2,

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

Received: March 2010

Revised: April 2010

Published: September 2010

Abstract / Introduction Related Papers Cited by

Abstract

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.

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Mathematics Subject Classification: 47J30, 35J50, 35J08, 37K40.

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