Eigenvalues for radially symmetric non-variational fully nonlinear operators

Maria J. Esteban (1) , Patricio Felmer (2) , Alexander Quaas (3)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
2 CMM - Centre de modélisation mathématique / Centro de Modelamiento Matemático [Santiago]
3 Departamento de Matematica [Valparaiso]

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 (and one dimensional) a much simpler theory can be established, and that the complete set of eigenvalues and eigenfuctions characterized by the number of zeroes can be obtained.

Mots clés: fully nonlinear operator; fully nonlinear equation; radially symmetric solutions; principle eigenvalue; multiple eigenvalues

Domaines: Equations aux dérivées partielles [math.AP]

Maria J. Esteban, Patricio Felmer, Alexander Quaas. Eigenvalues for radially symmetric non-variational fully nonlinear operators. Communications in Partial Differential Equations, 2010, 35 (9), pp.1716 - 1737. ⟨hal-00409427⟩