# 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…

## References

SHOWING 1-10 OF 28 REFERENCES

### Principal eigenvalues and the Dirichlet problem for fully nonlinear elliptic operators

- Mathematics
- 2008

### Principal eigenvalues and an anti-maximum principle for homogeneous fully nonlinear elliptic equations

- Mathematics
- 2009

### Multiplicity results for extremal operators through bifurcation

- Mathematics
- 2010

We study non-proper uniformly elliptic
fully nonlinear equations involving extremal operators of Pucci type. We prove the existence of all radial spectrum for this type of operators and
establish a…

### Two remarks on Monge-Ampere equations

- Mathematics
- 1985

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…

### Some aspects of nonlinear eigenvalue problems

- Mathematics
- 1973

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…