Abstract
We are concerned with a Dirichlet system, involving the Monge-Ampere
operator \det D^2u in a ball in
\mathbb{R}^N. Based on the Leray-Schauder degree, we
first obtain the existence of radial solutions for a class of
differential systems with general nonlinearities. In addition, we prove
that such a system admits positive solutions when nonlinearities satisfy
sub- or superlinear growth near origin. Finally, by using the lower and
upper solution method, and constructing the subsolution and
supersolution, we show the existence and multiplicity of nontrivial
radial solutions for Dirichlet systems with Monge-Ampere operator and
Lane-Emden type nonlinearities with two parameters.