The Method of Coupled Fixed Points and Coupled Quasisolutions When Working with ODE’s with Arguments of Bounded Variation - Rubén Figueroa (Abstract and Applied Analysis)
The aim of this paper is to show the use of the coupled quasisolutions method as a useful technique when dealing 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.