This paper deals with the lack of compactness in the nonlinear elliptic problem -Delta u+u = vertical bar u vertical bar(p-2)u in Omega, u > 0 in Omega, u = 0 on delta Omega, when Omega is un unbounded domain in R-n and 2 < p < 2n/(n - 2). In particular, a domain Omega is provided where non-converging Palais-Smale sequences exist at every energy level. Nevertheless, it is proved that the problem has infinitely many solutions on Omega.

Molle, R. (2006). Positive solutions for a nonlinear elliptic problem with strong lack of compactness. JOURNAL OF THE LONDON MATHEMATICAL SOCIETY, 74(2), 441-452 [10.1112/S002461070602309X].

Positive solutions for a nonlinear elliptic problem with strong lack of compactness

MOLLE, RICCARDO
2006-01-01

Abstract

This paper deals with the lack of compactness in the nonlinear elliptic problem -Delta u+u = vertical bar u vertical bar(p-2)u in Omega, u > 0 in Omega, u = 0 on delta Omega, when Omega is un unbounded domain in R-n and 2 < p < 2n/(n - 2). In particular, a domain Omega is provided where non-converging Palais-Smale sequences exist at every energy level. Nevertheless, it is proved that the problem has infinitely many solutions on Omega.
Pubblicato
Rilevanza internazionale
Articolo
Sì, ma tipo non specificato
Settore MAT/05 - Analisi Matematica
English
Con Impact Factor ISI
UNBOUNDED-DOMAINS; EXTERIOR DOMAINS; EXISTENCE
Molle, R. (2006). Positive solutions for a nonlinear elliptic problem with strong lack of compactness. JOURNAL OF THE LONDON MATHEMATICAL SOCIETY, 74(2), 441-452 [10.1112/S002461070602309X].
Molle, R
Articolo su rivista
File in questo prodotto:
Non ci sono file associati a questo prodotto.

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/2108/38909
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 3
  • ???jsp.display-item.citation.isi??? 3
social impact