We consider the Gelfand problem-Δu=ρ2V(x)euinΩu=0on∂Ω,where Ω is a planar domain and ρ is a positive small parameter. Under some conditions on the potential 0 < V∈ C∞(Ω ¯) , we provide the first examples of multiplicity for blowing-up solutions at a given point in Ω as ρ→ 0. The argument is based on a refined Lyapunov–Schmidt reduction and the computation of the degree of a finite-dimensional map.

Battaglia, L., Grossi, M., Pistoia, A. (2019). Non-uniqueness of blowing-up solutions to the Gelfand problem. CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 58(5) [10.1007/s00526-019-1607-z].

Non-uniqueness of blowing-up solutions to the Gelfand problem

Battaglia L.;
2019-01-01

Abstract

We consider the Gelfand problem-Δu=ρ2V(x)euinΩu=0on∂Ω,where Ω is a planar domain and ρ is a positive small parameter. Under some conditions on the potential 0 < V∈ C∞(Ω ¯) , we provide the first examples of multiplicity for blowing-up solutions at a given point in Ω as ρ→ 0. The argument is based on a refined Lyapunov–Schmidt reduction and the computation of the degree of a finite-dimensional map.
2019
Battaglia, L., Grossi, M., Pistoia, A. (2019). Non-uniqueness of blowing-up solutions to the Gelfand problem. CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 58(5) [10.1007/s00526-019-1607-z].
File in questo prodotto:
File Dimensione Formato  
1902.03484.pdf

accesso aperto

Dimensione 343.91 kB
Formato Adobe PDF
343.91 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: https://hdl.handle.net/11590/361911
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 4
  • ???jsp.display-item.citation.isi??? 4
social impact