Two generalizations of the notion of principal eigenvalue for elliptic operators in ℝNare examined in this paper. We prove several results comparing these two eigenvalues in various settings: general operators in dimension one; self-adjoint operators; and "limit periodic" operators. These results apply to questions of existence and uniqueness for some semilinear problems in the whole space. We also indicate several outstanding open problems and formulate some conjectures. © European Mathematical Society 2006.

On the principal eigenvalue of elliptic operators in ℝNand applications / Berestycki, H.; Rossi, L.. - In: JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY. - ISSN 1435-9855. - 8:2(2006), pp. 195-215. [10.4171/JEMS/47]

On the principal eigenvalue of elliptic operators in ℝNand applications

Rossi L.
2006

Abstract

Two generalizations of the notion of principal eigenvalue for elliptic operators in ℝNare examined in this paper. We prove several results comparing these two eigenvalues in various settings: general operators in dimension one; self-adjoint operators; and "limit periodic" operators. These results apply to questions of existence and uniqueness for some semilinear problems in the whole space. We also indicate several outstanding open problems and formulate some conjectures. © European Mathematical Society 2006.
2006
Elliptic operators; generalized principal eigenvalue in ℝ; n; limit periodic operators; principal eigenvalue
01 Pubblicazione su rivista::01a Articolo in rivista
On the principal eigenvalue of elliptic operators in ℝNand applications / Berestycki, H.; Rossi, L.. - In: JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY. - ISSN 1435-9855. - 8:2(2006), pp. 195-215. [10.4171/JEMS/47]
File allegati a questo prodotto
File Dimensione Formato  
Berestychi_preprint_On-the-principal-eigenvalue_2006.pdf

accesso aperto

Tipologia: Documento in Pre-print (manoscritto inviato all'editore, precedente alla peer review)
Licenza: Creative commons
Dimensione 254.12 kB
Formato Adobe PDF
254.12 kB Adobe PDF
Berestychi_On-the-principal-eigenvalue_2006.pdf

solo gestori archivio

Tipologia: Versione editoriale (versione pubblicata con il layout dell'editore)
Licenza: Tutti i diritti riservati (All rights reserved)
Dimensione 181.99 kB
Formato Adobe PDF
181.99 kB Adobe PDF   Contatta l'autore

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/11573/1464028
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 48
  • ???jsp.display-item.citation.isi??? 48
social impact