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.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.