  The aim of this paper is to show the use of the coupled quasisolutions method
as a useful technique when treating with ordinary differential equations with
functional arguments of bounded variation. We will do this by looking for
solutions for a first-order ordinary differential equation with an advanced
argument of bounded variation. The main trick is to use the Jordan
decomposition of this argument in a nondecreasing part and a nonincreasing one.
As a necessary step, we will also talk about coupled fixed points of
multivalued operators.
