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ON VOLTERRA OPERATOR INCLUSIONS AND DIFFERENTIAL INCLUSIONS WITH DEVIATING ARGUMENT

Annotation

We obtained conditions for solvability of operator inclusions with abstract Volterra operators and continuous dependence of the solutions on a parameter. These results were implemented to investigation of a Cauchy problem for a functional-differential inclusion with deviating argument.

Keywords

Volterra operator inclusions; functional-differential inclusions; inclusions with deviating argument; existence of solutions; continuous dependence on parameters

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DOI

10.20310/1810-0198-2017-22-3-501-507

UDC

517.988.5, 517.911.5

Pages

501-507

References

1. Tikhonov А.N. О funkcional’nykh uravneniyah tipa Volterra i ih primeneniyah k nekotorym zadacham matematicheskoi fiziki // Bull. Moscow University. Section A. 1938. № 8. V. 1. P. 1–25. 2. Zhukovskiy Е.S. Nepreryvnaya zavisimost’ ot parametrov resheniy uravneniy Volterra // Sbornik Mathematics. 2006. V. 197. № 10. P. 33–56. 3. Burlakov Е.О., Zhukovskiy Е.S. Nepreryvnaya zavisimost’ ot parametrov resheniy uravneniy Volterra’s lokal’no szhimayushimi operatorami // Izvestija VUZov. Matematika. 2010. № 8. P. 16–29. 4. Bulgakov A.I., Malyutina E.V., Filippova O.V. Apriornaya ogranichennost’ i nepreryvnaya zavisimost’ ot parametrov mnozhestva fazovykh traektoriy upravlyaemoy sistemy s fazovymi ogranicheniyami po upravleniyu // Vestnik Tambovskogo universiteta. Seriya Estestvennye i tekhnicheskie nauki – Tambov University Reports. Series: Natural and Technical Sciences. Tambov, 2011. V. 16. Iss. 1. P. 38–42. 5. Bulgakov A.I., Malyutina E.V., Filippova O.V. Differentsial’noe vklyuchenie s zapazdyvaniem, zavisyashim ot parametrov // Vestnik Tambovskogo universiteta. Seriya Estestvennye i tekhnicheskie nauki – Tambov University Reports. Series: Natural and Technical Sciences. Tambov, 2012. V. 17. Iss. 1. P. 28–31. 6. Zhukovskiy Е.S. Obobshenno volterrovye operatory v metricheskih prostranstvah // Vestnik Tambovskogo universiteta. Seriya Estestvennye i tekhnicheskie nauki – Tambov University Reports. Series: Natural and Technical Sciences. Tambov, 2009. V. 14. Iss. 3. P. 501–508.

Received

2017-01-10

Section of issue

Functional-differential equations and inclusions and their applications to mathematical modeling

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