In this work we study the existence of nodal solutions for the problem -Δu=λueu2+|u|pinΩ,u=0on∂Ω,where Ω ⊆ R2 is a bounded smooth domain and p→ 1 +. If Ω is a ball, it is known that the case p= 1 defines a critical threshold between the existence and the non-existence of radially symmetric sign-changing solutions. In this work we construct a blowing-up family of nodal solutions to such problem as p→ 1 +, when Ω is an arbitrary domain and λ is small enough. As far as we know, this is the first construction of sign-changing solutions for a Moser–Trudinger critical equation on a non-symmetric domain.

Bubbling nodal solutions for a large perturbation of the Moser–Trudinger equation on planar domains / Grossi, M.; Mancini, G.; Naimen, D.; Pistoia, A.. - In: MATHEMATISCHE ANNALEN. - ISSN 0025-5831. - (2020). [10.1007/s00208-020-01975-w]

Bubbling nodal solutions for a large perturbation of the Moser–Trudinger equation on planar domains

Grossi M.
;
Mancini G.;Pistoia A.
2020

Abstract

In this work we study the existence of nodal solutions for the problem -Δu=λueu2+|u|pinΩ,u=0on∂Ω,where Ω ⊆ R2 is a bounded smooth domain and p→ 1 +. If Ω is a ball, it is known that the case p= 1 defines a critical threshold between the existence and the non-existence of radially symmetric sign-changing solutions. In this work we construct a blowing-up family of nodal solutions to such problem as p→ 1 +, when Ω is an arbitrary domain and λ is small enough. As far as we know, this is the first construction of sign-changing solutions for a Moser–Trudinger critical equation on a non-symmetric domain.
2020
Moser-Trudinger; blow-up; nodal solutions; perturbations; bubbles
01 Pubblicazione su rivista::01a Articolo in rivista
Bubbling nodal solutions for a large perturbation of the Moser–Trudinger equation on planar domains / Grossi, M.; Mancini, G.; Naimen, D.; Pistoia, A.. - In: MATHEMATISCHE ANNALEN. - ISSN 0025-5831. - (2020). [10.1007/s00208-020-01975-w]
File allegati a questo prodotto
File Dimensione Formato  
Grossi_Bubbling-nodal_2020.pdf

solo gestori archivio

Tipologia: Versione editoriale (versione pubblicata con il layout dell'editore)
Licenza: Tutti i diritti riservati (All rights reserved)
Dimensione 596.42 kB
Formato Adobe PDF
596.42 kB Adobe PDF   Contatta l'autore
Grossi_preprint_Bubbling-nodal_2020.pdf

accesso aperto

Tipologia: Documento in Pre-print (manoscritto inviato all'editore, precedente alla peer review)
Licenza: Tutti i diritti riservati (All rights reserved)
Dimensione 579.52 kB
Formato Unknown
579.52 kB Unknown

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/11573/1423477
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 3
  • ???jsp.display-item.citation.isi??? 3
social impact