Functional Differential Equations in the Space of Functions of Bounded Variation / Sesekin A. N.,Fetisova Yu. V. // PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS. - 2010. - V. 269, l. 1. - P. S258-S265.

ISSN/EISSN:

0081-5438 / 1531-8605

Type:

Article

Abstract:

For nonlinear systems of functional differential equations with a generalized action on the right-hand side, the notion of a solution based on the closure of smooth solutions in the space of functions of bounded variation is formalized. Sufficient conditions for the existence and uniqueness of the solution are obtained. For linear systems with distributed delay and generalized action in the system matrix, conditions for the existence of a solution and the Cauchy formula for representing the solution are derived.

Author keywords:

generalized action; discontinuous solution; functional differential equation; delay

DOI:

10.1134/S0081543810060210

Web of Science ID:

ISI:000209701100021

Соавторы в МНС:

—

Другие поля

Поле	Значение
Month	JUL
Publisher	MAIK NAUKA/INTERPERIODICA/SPRINGER
Address	233 SPRING ST, NEW YORK, NY 10013-1578 USA
Language	English
EISSN	1531-8605
Research-Areas	Mathematics
Web-of-Science-Categories	Mathematics, Applied; Mathematics
Author-Email	sesekin@imm.uran.ru j.v.fetisova@imm.uran.ru
ORCID-Numbers	Sesekin, Alexander/0000-0002-1339-9044
Funding-Acknowledgement	Program for Integration Fundamental Research of the Ural Division; Siberian Branch of the Russian Academy of Sciences ``Qualitative and Numerical Analysis of Evolution Equations and Controlled Systems{''}
Funding-Text	This work was supported by the Program for Integration Fundamental Research of the Ural Division and Siberian Branch of the Russian Academy of Sciences ``Qualitative and Numerical Analysis of Evolution Equations and Controlled Systems.{''}
Number-of-Cited-References	18
Journal-ISO	Proc. Steklov Inst. Math.
Doc-Delivery-Number	V43SM