Eigenvalues for Radially Symmetric Fully Nonlinear Operators

Esteban, Maria J.; Felmer, Patricio; Quaas, Alexander

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

Number

Publisher

Taylor & Francis

Pages

1716-1737

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