We consider the SU(3) singular Toda system on a compact surface (Σ,g) (-δu1=2ρ1(h1eu1∫Σh1eu1dVg-1)-ρ2(h2eu2∫Σh2eu2dVg-1)-4π∑m=1Mα1m(δpm-1)-δu2=2ρ2(h2eu2∫Σh2eu2dVg-1)-ρ1(h1eu1∫Σh1eu1dVg-1)-4π∑m=1Mα2m(δpm-1), where hi are smooth positive functions on Σ, ρi∈R+, pm∈Σ and αim>-1.We give both existence and non-existence results under some conditions on the parameters ρi and αim. Existence results are obtained using variational methods, which involve a geometric inequality of new type; non-existence results are obtained using blow-up analysis and localized Pohožaev-type identities.

Existence and non-existence results for the SU(3) singular Toda system on compact surfaces

MALCHIODI, ANDREA
2016

Abstract

We consider the SU(3) singular Toda system on a compact surface (Σ,g) (-δu1=2ρ1(h1eu1∫Σh1eu1dVg-1)-ρ2(h2eu2∫Σh2eu2dVg-1)-4π∑m=1Mα1m(δpm-1)-δu2=2ρ2(h2eu2∫Σh2eu2dVg-1)-ρ1(h1eu1∫Σh1eu1dVg-1)-4π∑m=1Mα2m(δpm-1), where hi are smooth positive functions on Σ, ρi∈R+, pm∈Σ and αim>-1.We give both existence and non-existence results under some conditions on the parameters ρi and αim. Existence results are obtained using variational methods, which involve a geometric inequality of new type; non-existence results are obtained using blow-up analysis and localized Pohožaev-type identities.
Settore MAT/05 - Analisi Matematica
Liouville-type equations; Min-max solutions; Non-existence results; Toda system;
File in questo prodotto:
File Dimensione Formato  
BM-JFA-PP.pdf

accesso aperto

Descrizione: BM-JFA-PP
Tipologia: Accepted version (post-print)
Licenza: Creative commons
Dimensione 832.58 kB
Formato Adobe PDF
832.58 kB Adobe PDF Visualizza/Apri
1-s2.0-S0022123615004942-main.pdf

Accesso chiuso

Tipologia: Published version
Licenza: Non pubblico
Dimensione 1.24 MB
Formato Adobe PDF
1.24 MB Adobe PDF   Visualizza/Apri   Richiedi una copia

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: http://hdl.handle.net/11384/64420
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 16
  • ???jsp.display-item.citation.isi??? 16
social impact