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.
Non-uniqueness of blowing-up solutions to the Gelfand problem / Battaglia, L.; Grossi, M.; Pistoia, A.. - In: CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS. - ISSN 0944-2669. - 58:5(2019). [10.1007/s00526-019-1607-z]
Non-uniqueness of blowing-up solutions to the Gelfand problem
Grossi M.
;Pistoia A.
2019
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 | Dimensione | Formato | |
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