  The concept of nonlinear split ordered variational inequality problems on
partially ordered vector spaces is a natural extension of linear split vector
variational inequality problems on Banach spaces. The results about nonlinear
split ordered variational inequality problems are immediately applied to
solving nonlinear split vector optimization problems. In this paper, we prove
the solvability of some nonlinear split ordered variational inequality problems
by using some fixed point theorems on partially ordered spaces, in which the
considered mappings may not be required to have any type of continuity and they
just satisfy some order-monotonic conditions. As applications of the results
about nonlinear split ordered variational inequality problems, we study
solvability of some nonlinear split variational inequality problems and linear
split variational inequality problems on partially ordered vector spaces and
partially ordered Banach spaces.
