  In this paper we study the following eigenvalue boundary value problem for
Monge-Amp\`{e}re equations: {equation} \{{array}{l} \det(D^2u)=\lambda^N
f(-u)\,\, \text{in}\,\, \Omega, u=0,\,\text{on}\,\, \partial \Omega. {array}.
{equation} We establish the unilateral global bifurcation results for the
problem with $f(u)=u^N+g(u)$ and $\Omega$ being the unit ball of
$\mathbb{R}^N$. More precisely, under some natural hypotheses on the
perturbation function $g:\mathbb{R}\rightarrow\mathbb{R}$, we show that
$(\lambda_1,0)$ is a bifurcation point of the problem and there are two
distinct unbounded continua of one-sign solutions, where $\lambda_1$ is the
first eigenvalue of the problem with $f(u)=u^N$. As the applications of the
above results, we consider with determining interval of $\lambda$, in which
there exist solutions for this problem in unit ball. Moreover, we also get some
results on the existence and nonexistence of convex solutions for this problem
in general domain by domain comparison method.
