We provide the asymptotic behavior of solutions, at the singularity and at infinity, for a class of subelliptic Dirichlet problems with Hardy perturbation and critical nonlinearity of the type −Lαu−μψ^2/d^2u=K(z)|u|^(2∗−2)u in Ω, where Lα=Δx+|x|2αΔy, α>0 is the so-called Grushin operator, Ω is an open subset of R^N, 0∈Ω, d is the gauge norm naturally associated with Lα, ψ:=|∇αd|, where ∇α is the Grushin gradient, K∈L∞ and 0≤μ< mus$, where mus is the best Hardy constant for Lα. Furthermore, we establish some Pohozaev-type non-existence results.

Asymptotic estimates and nonexistence results for critical problems with Hardy term involving Grushin-type operators

Annunziata Loiudice
2019

Abstract

We provide the asymptotic behavior of solutions, at the singularity and at infinity, for a class of subelliptic Dirichlet problems with Hardy perturbation and critical nonlinearity of the type −Lαu−μψ^2/d^2u=K(z)|u|^(2∗−2)u in Ω, where Lα=Δx+|x|2αΔy, α>0 is the so-called Grushin operator, Ω is an open subset of R^N, 0∈Ω, d is the gauge norm naturally associated with Lα, ψ:=|∇αd|, where ∇α is the Grushin gradient, K∈L∞ and 0≤μ< mus$, where mus is the best Hardy constant for Lα. Furthermore, we establish some Pohozaev-type non-existence results.
File in questo prodotto:
File Dimensione Formato  
Loiudice2019_Article_AsymptoticEstimatesAndNonexist.pdf

non disponibili

Tipologia: Documento in Versione Editoriale
Licenza: NON PUBBLICO - Accesso privato/ristretto
Dimensione 429.7 kB
Formato Adobe PDF
429.7 kB Adobe PDF   Visualizza/Apri   Richiedi una copia
Loiudice_ Grushin Hardy_preprint.pdf

accesso aperto

Tipologia: Documento in Pre-print
Licenza: Creative commons
Dimensione 258.6 kB
Formato Adobe PDF
258.6 kB Adobe PDF Visualizza/Apri

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/11586/232670
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 5
  • ???jsp.display-item.citation.isi??? 5
social impact