We consider the Brezis-Nirenberg problem -Delta u = lambda u + vertical bar u vertical bar(p-1) u in Omega, u = 0 on partial derivative Omega, where Omega is a smooth bounded domain in R-N, N >= 3, p = N+2/N-2 and lambda > 0. We prove that, if Omega is symmetric and N = 4, 5, there exists a sign-changing solution whose positive part concentrates and blowsup at the center of symmetry of the domain, while the negative part vanishes, as lambda -> lambda(1), where lambda(1) = lambda(1)( Omega) denotes the first eigenvalue of -Delta on Omega, with zero Dirichlet boundary condition.
Sign-changing blowing-up solutions for the Brezis-Nirenberg problem in dimensions four and five / A. Iacopetti, G. Vaira. - In: ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA. CLASSE DI SCIENZE. - ISSN 0391-173X. - 18:1(2018), pp. 1-38. [10.2422/2036-2145.201602_003]
Sign-changing blowing-up solutions for the Brezis-Nirenberg problem in dimensions four and five
A. Iacopetti;
2018
Abstract
We consider the Brezis-Nirenberg problem -Delta u = lambda u + vertical bar u vertical bar(p-1) u in Omega, u = 0 on partial derivative Omega, where Omega is a smooth bounded domain in R-N, N >= 3, p = N+2/N-2 and lambda > 0. We prove that, if Omega is symmetric and N = 4, 5, there exists a sign-changing solution whose positive part concentrates and blowsup at the center of symmetry of the domain, while the negative part vanishes, as lambda -> lambda(1), where lambda(1) = lambda(1)( Omega) denotes the first eigenvalue of -Delta on Omega, with zero Dirichlet boundary condition.File | Dimensione | Formato | |
---|---|---|---|
Sign-changing_Blowing_BN_Dim4_5_postprint.pdf
accesso riservato
Tipologia:
Post-print, accepted manuscript ecc. (versione accettata dall'editore)
Dimensione
438.05 kB
Formato
Adobe PDF
|
438.05 kB | Adobe PDF | Visualizza/Apri Richiedi una copia |
1-Iacopetti_Vaira.pdf
accesso riservato
Tipologia:
Publisher's version/PDF
Dimensione
836.95 kB
Formato
Adobe PDF
|
836.95 kB | Adobe PDF | Visualizza/Apri Richiedi una copia |
Pubblicazioni consigliate
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.