# Global branches of solutions for a class of non uniformly fully nonlinear elliptic equations

## TL;DR

This paper investigates the global solution structure of a class of fully nonlinear elliptic equations, establishing bifurcation results and analyzing eigenvalue behaviors under singular perturbations.

## Contribution

It introduces new global bifurcation results for non-uniform fully nonlinear elliptic equations and characterizes eigenvalues in singular perturbation contexts.

## Key findings

- Existence of simple eigenvalues for perturbed problems
- Asymptotic behavior of eigenvalues analyzed
- Global bifurcation branches of positive smooth solutions established

## Abstract

We consider singular perturbations of eigenvalue problems. We prove that to these problems correspond simple eigenvalues and we study their asymptotic behavior. As a result, we prove global bifurcation results for non uniformly and fully nonlinear elliptic equations. These equations are defined on smooth enough bounded domains and the solutions belonging in these branches are smooth and positive.