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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
External document link
http://arxiv.org/abs/0908.1060v1
Date
2010
Journal name
Communications in Partial Differential Equations
Volume
35
Number
9
Publisher
Taylor & Francis
Pages
1716-1737
Publication identifier
http://dx.doi.org/10.1080/03605301003674848
Metadata
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Author(s)
Esteban, Maria J. cc
Felmer, Patricio
Quaas, Alexander
Abstract (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.
Subjects / Keywords
Fully nonlinear equation; Fully nonlinear operator; Multiple eigenvalues; Principal eigenvalue; Radially symmetric solutions

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