Eigenvalues for radially symmetric non-variational fully nonlinear operators

Details Eigenvalues for radially symmetric non-variational fully nonlinear operators Eigenvalues for radially symmetric non-variational fully nonlinear operators

2009-08-07

arxiv.org/abs/0908.1060v1

Mathematics

Analysis of PDEs

Scientific paper

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.

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