Generalized eigenvalues for fully tnonlinear singular or degenerate operators in the radial case

TL;DR

This paper extends the theory of generalized eigenvalues for fully nonlinear, singular, or degenerate operators in the radial case, proving the existence of infinitely many simple, isolated eigenvalues.

Contribution

It establishes the existence of an infinite sequence of eigenvalues for a class of fully nonlinear operators in the radial setting, expanding previous results for specific operators.

Findings

Existence of infinitely many eigenvalues

Eigenvalues are simple and isolated

Completes previous results for specific operators

Abstract

In this paper we extend some existence's results concerning the generalized eigenvalues for fully nonlinear operators singular or degenerate. We consider the radial case and we prove the existence of an infinite number of eigenvalues, simple and isolated. This completes the results obtained by the author with Isabeau Birindelli for the first eigenvalues in the radial case, and the results obtained for the Pucci's operator by Busca Esteban and Quaas and for the $p$-Laplace operator by Del Pino and Manasevich.