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arXiv · 1305.3266

The method of coupled fixed points and coupled quasisolutions when working with ODE's with arguments of bounded variation

Rubén Figueroa
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Abstract

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.

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Rubén Figueroa. 2013-05-14. The method of coupled fixed points and coupled quasisolutions when working with ODE's with arguments of bounded variation. https://arxiv.org/abs/1305.3266

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