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Eigenvalues for Radially Symmetric Fully Nonlinear Operators

Esteban, Maria J.; Felmer, Patricio; Quaas, Alexander (2010), Eigenvalues for Radially Symmetric Fully Nonlinear Operators, Communications in Partial Differential Equations, 35, 9, p. 1716-1737. http://dx.doi.org/10.1080/03605301003674848

Type
Article accepté pour publication ou publié
Lien vers un document non conservé dans cette base
http://arxiv.org/abs/0908.1060v1
Date
2010
Nom de la revue
Communications in Partial Differential Equations
Volume
35
Numéro
9
Éditeur
Taylor & Francis
Pages
1716-1737
Identifiant publication
Métadonnées
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Auteur(s)
Esteban, Maria J. cc
Felmer, Patricio
Quaas, Alexander
Résumé (EN)
In this paper we present an elementary theory about the existence of eigenvalues for fully nonlinear radially symmetric 1-homogeneous operators. A general theory for first eigenvalues and eigenfunctions of 1-homogeneous fully nonlinear operators exists in the framework of viscosity solutions. Here we want to show that for the radially symmetric operators or in the one dimensional case a much simpler theory, based on ode and degree theory arguments, can be established. We obtain the complete set of eigenvalues and eigenfunctions characterized by the number of zeroes.
Mots-clés
Fully nonlinear equation; Fully nonlinear operator; Multiple eigenvalues; Principal eigenvalue; Radially symmetric solutions