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Corpus ID: 10181783

Eigenvalues for radially symmetric non-variational fully nonlinear operators

@article{Esteban2009EigenvaluesFR,
title={Eigenvalues for radially symmetric non-variational fully nonlinear operators},
author={Maria J. Esteban and Patricio Felmer and Alexander M. Quaas},
journal={arXiv: Analysis of PDEs},
year={2009}
}

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… Expand

SummaryWe consider real Monge-Ampère equations and we present two new properties of these equations. First, we show the existence of the «first eigenvalue of Monge-Ampère equation» i.e. we show the… Expand

where k G. R and u E £ . A solution of (0.1) is a pair (A, M ) £ H X £. Equations of the form (0.1) are generally called nonlinear eigenvalue problems. As has been amply demonstrated at this… Expand