Abstract
The present project of scientific research concerns about the theory of impulsive functional dynamic equations on time scales to be developed at the department of mathematics and computation at University of São Paulo in Ribeirão Preto. The main goal of this project is to develop the theory of impulsive functional dynamic equations on time scales. This theory has been shown a powerful tool for applications in several fields of knowledge such as economics, biology, physics, engineer, among others. It is due to the fact that this theory unifies the discrete and continuous case as well as other cases depending on the chosen time scale. This project is divided in 5 sub-projects. In the first and second ones, we intend to investigate the existence of periodic and almost periodic solutions of impulsive functional dynamic equations on time scales as well as to obtain instability results for these equations. In the third sub-project, our goal is to study the equations called neutral functional dynamic equations on time scales with impulses, obtaining results such as existence and uniqueness and continuous dependence. Furthermore, in the fourth sub-project, we investigate the abstract functional dynamic equations on time scales, by using semigroup theory on time scales, which was recently introduced in the literature. We study the qualitative properties of their solutions. And finally, in the last sub-project, we investigate some applications of dynamic equations on time scales to economic problems. More precisely, we focus our investigation in the study of the model known as Keynesian-Cross model with lagged income. (AU)
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