For domains of first kind we describe the qualitative behavior of the global bifurcation diagram of the unbounded branch of solutions of the Gelfand problem crossing the origin. At least to our knowledge this is the first result about the exact monotonicity of the branch of nonminimal solutions which is not just concerned with radial solutions and/or with symmetric domains. Toward our goal we parametrize the branch not by the L ∞ -norm of the solutions but by the energy of the associated mean field problem. The proof relies on a refined spectral analysis of mean-field-type equations and some surprising properties of the quantities triggering the monotonicity of the Gelfand parameter.

Bartolucci, D., Jevnikar, A. (2021). On the global bifurcation diagram of the Gelfand problem. ANALYSIS & PDE, 14(8), 2409-2426.

On the global bifurcation diagram of the Gelfand problem

Bartolucci, D.
Membro del Collaboration Group
;
2021-01-01

Abstract

For domains of first kind we describe the qualitative behavior of the global bifurcation diagram of the unbounded branch of solutions of the Gelfand problem crossing the origin. At least to our knowledge this is the first result about the exact monotonicity of the branch of nonminimal solutions which is not just concerned with radial solutions and/or with symmetric domains. Toward our goal we parametrize the branch not by the L ∞ -norm of the solutions but by the energy of the associated mean field problem. The proof relies on a refined spectral analysis of mean-field-type equations and some surprising properties of the quantities triggering the monotonicity of the Gelfand parameter.
2021
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore MAT/05 - ANALISI MATEMATICA
English
Con Impact Factor ISI
global bifurcation; Gelfand problem; Rabinowitz continuum; mean field equation
https://arxiv.org/abs/1901.06700
Bartolucci, D., Jevnikar, A. (2021). On the global bifurcation diagram of the Gelfand problem. ANALYSIS & PDE, 14(8), 2409-2426.
Bartolucci, D; Jevnikar, A
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/283587
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