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.
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].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11590/361911
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