Vadim Z. Tsalyuk
This paper studies the functional differential equation
where is a generalized derivative, and and are functions of bounded variation. A solution is defined by the difference being absolutely continuous and satisfying the inclusion
Here, the integral in the right is the multivalued Stieltjes integral presented in  (in this article we review and extend the results in ). We show that the solution set for the initial-value problem is nonempty, compact, and convex. A solution is said to have memory if there exists the function such that , , for , and , where Lebesgue-Stieltjes integral is used. We show that such solutions form a nonempty, compact, and convex set. It is shown that solutions with memory obey the Cauchy-type formula
Submitted June 14, 2003. Published October 13, 2003.
Math Subject Classifications: 26A42, 28B20, 34A60.
Key Words: Stieltjes integral, function of bounded variation, multivalued integral, linear functional differential equation.
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| Vadim Z. Tsalyuk |
Kuban State University
Stavropol'skaya 149, Krasnodar 350040, Russia
http://public.kubsu.ru/vts (in Russian)
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