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Home » Issues » Archive of Issues » 2013 - 3 issue » pp. 49-64

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Russia Tambov
Year
2013
Issue
3
Pages
49-64
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Section Mathematics
Title Well-posed solvability of control problems for systems of implicit differential equations
Author(-s) Pluzhnikova E.A.a
Affiliations Tambov State Universitya
Abstract Theorems on solvability, estimates of solutions, and well-posed solvability of equations with covering mappings in the product of metric spaces are formulated. Conditions for the Nemytskii operator to be a covering operator in functional spaces are considered. Statements about covering mappings are applied to studying the controlled systems described by ordinary differential equations unsolved for the derivative. For controlled differential systems with mixed constraints on control and an additional constraint on the solution's derivative, conditions of solvability are received as well as solutions' estimates, the question of continuous dependence of solutions on parameters is investigated.
Keywords covering mappings, metric spaces, implicit differential equations, well-posed solvability, controlled systems
UDC 517.922, 517.977.1, 517.988.6
MSC 34A09, 34H05, 47J05
DOI 10.20537/vm130305
Received 19 April 2013
Language Russian
Citation Pluzhnikova E.A. Well-posed solvability of control problems for systems of implicit differential equations, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2013, issue 3, pp. 49-64.
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