publication . Article . 2014

Linear measure functional differential equations with infinite delay

Giselle Antunes Monteiro; Antonín Slavík;
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  • Published: 01 Jan 2014 Journal: Mathematische Nachrichten, volume 287, pages 1,363-1,382 (issn: 0025-584X, Copyright policy)
  • Publisher: Wiley
  • Country: Czech Republic
Abstract
We use the theory of generalized linear ordinary differential equations in Banach spaces to study linear measure functional differential equations with infinite delay. We obtain new results concerning the existence, uniqueness, and continuous dependence of solutions. Even for equations with a finite delay, our results are stronger than the existing ones. Finally, we present an application to functional differential equations with impulses.
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free text keywords: General Mathematics, measure functional differential equations, generalized ordinary differential equations, Kurzweil-Stieltjes integral, Mathematics, Numerical partial differential equations, Delay differential equation, Mathematical analysis, C0-semigroup, Differential algebraic equation, Stochastic partial differential equation, Exponential integrator, Linear differential equation, Distributed parameter system
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