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

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.