Global bifurcation and convex solutions for the Monge-Ampère equation

We study the following Monge-Ampère equation{(det⁡(D2u))1N=λf(−u)inΩ,u=0on∂Ω 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.