We generalise the semi-Riemannian Morse index theorem to elliptic systems of partial differential equations on star-shaped domains. Moreover, we apply our theorem to bifurcation from a branch of trivial solutions of semilinear systems, where the bifurcation parameter is introduced by shrinking the domain to a point. This extends recent results of the authors for scalar equations.

A Morse-Smale index theorem for indefinite elliptic systems and bifurcation.

PORTALURI, Alessandro;
2015-01-01

Abstract

We generalise the semi-Riemannian Morse index theorem to elliptic systems of partial differential equations on star-shaped domains. Moreover, we apply our theorem to bifurcation from a branch of trivial solutions of semilinear systems, where the bifurcation parameter is introduced by shrinking the domain to a point. This extends recent results of the authors for scalar equations.
2015
258
5
1715
1748
http://arxiv.org/abs/1408.1419
Maslov index, Spectral flow, Bifurcation theory, Elliptic PDE's
Portaluri, Alessandro; Waterstraat, Nils
File in questo prodotto:
File Dimensione Formato  
JDE-Nils.pdf

Accesso riservato

Tipo di file: PDF EDITORIALE
Dimensione 473.75 kB
Formato Adobe PDF
473.75 kB Adobe PDF   Visualizza/Apri   Richiedi una copia
IndEllSys.pdf

Accesso aperto

Tipo di file: POSTPRINT (VERSIONE FINALE DELL’AUTORE)
Dimensione 423.12 kB
Formato Adobe PDF
423.12 kB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2318/1520714
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 18
  • ???jsp.display-item.citation.isi??? 12
social impact