Abstract

We study uniformly elliptic fully nonlinear equations of the type F (D2u, Du, u, x) = f (x). We - show that convex positively 1-ho mogeneous operators possess two principal eigenvalues and eigenfunctions, and study these objects; - obtain existence and uniqueness results for non-proper operators whose principal eigenvalues (in some cases, only one of them) are positive; - obtain an existence result for non-proper Isaac's equations. © 2005 Académie des sciences. Published by Elsevier SAS. All rights reserved.