ZERO ORDER PERTURBATIONS TO FULLY NONLINEAR EQUATIONS: COMPARISON, EXISTENCE AND UNIQUENESS

We study existence of solutions to [Formula: see text] where F is elliptic and homogeneous of degree m, and either f(λ,u) = λ uqor f(λ,u) = λ uq+ ur, for 0 < q < m < r, and λ > 0. Furthermore, in the first case, we obtain that the solution is unique as a consequence of a comparison principle up to the boundary. Several examples, including uniformly elliptic operators and the infinity-laplacian, are considered.