Abstract

We study the equation {-MλΛ + (D 2u) = f(x, u) in Ω, u = 0 on ∂Ω, in general smooth bounded domain Ω, and show it possesses nontrivial solutions provided that: • f is sublinear, or • f is superlinear and the equation admits a priori bounds. The existence result in the superlinear case is based on a new Liouville type theorem for -Mλ,Λ + (D 2u) = up in a half-space. Copyright © Taylor & Francis Group, LLC.