Global bifurcation and convex solutions for the Monge-Ampere equation

We study the following Monge-Ampere equation {(det (D(2)u))(1/N) = lambda f(-u) in Omega u = 0 on partial derivative Omega by bifurcation technique. We establish some results about the existence, nonexistence, uniqueness and multiplicity of convex solutions for this problem. Our results generalize and improve many important known results from previous literature. (C) 2020 Elsevier Inc. All rights reserved.