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This article is cited in 11 scientific papers (total in 11 papers)
On the theory of the Cauchy problem for an ordinary differential equation with discontinuous right-hand side
V. V. Filippov
Abstract:
An apparatus is developed for proving theorems on the existence of a solution of the Cauchy problem and on continuous dependence of solutions on the initial conditions and parameters, applicable to situations not covered by known results on this subject.
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Russian Academy of Sciences. Sbornik. Mathematics, 1995, 83:2, 383–403
Bibliographic databases:
  
UDC:
517.911
MSC: 34A12
Received: 01.04.1993
Citation:
V. V. Filippov, “On the theory of the Cauchy problem for an ordinary differential equation with discontinuous right-hand side”, Mat. Sb., 185:11 (1994), 95–118; Russian Acad. Sci. Sb. Math., 83:2 (1995), 383–403
Citation in format AMSBIB
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\transl
\jour Russian Acad. Sci. Sb. Math.
\yr 1995
\vol 83
\issue 2
\pages 383--403
\crossref{https://doi.org/10.1070/SM1995v083n02ABEH003597}
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http://mi.mathnet.ru/eng/msb942 http://mi.mathnet.ru/eng/msb/v185/i11/p95
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This publication is cited in the following articles:
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Filippov V., “Differential-Inclusions of 2nd-Order - Cauchy-Problem, Periodic-Solutions”, Dokl. Akad. Nauk, 344:3 (1995), 311–314
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V. V. Filippov, “Existence of periodic solutions”, Math. Notes, 61:5 (1997), 644–656
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Filippov V., “On the Theory of the Cauchy Problem for an Ordinary Differential Equation with Discontinuities with Respect to Space Variables”, Differ. Equ., 33:7 (1997), 888–894
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Filippov A., “Stability and Instability by the First Approximation”, Differ. Equ., 36:4 (2000), 529–539
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V. V. Filippov, “Optimal Solution Space and Regularization of Equations with Discontinuities in the Space Variables”, Math. Notes, 70:3 (2001), 413–421
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Filippov, VV, “The Leray-Schauder method vs translation along the trajectories: Which is better in the theory of boundary value problems?”, Differential Equations, 37:8 (2001), 1097
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V. V. Filippov, “On the existence of periodic solutions of equations with strongly increasing principal part”, Sb. Math., 193:11 (2002), 1707–1729
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Filippov V., “On a Scalar Equation with Discontinuous Right-Hand Side and the Uniqueness Theorem”, Differ. Equ., 38:10 (2002), 1435–1445
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A. V. Zuev, “On periodic solutions of ordinary differential equations with discontinuous right-hand side”, Math. Notes, 79:4 (2006), 518–527
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D. A. Serkov, “Minimizatsiya riska pri funktsionalnykh ogranicheniyakh na dinamicheskuyu pomekhu”, Izv. IMI UdGU, 2014, no. 2(44), 3–95
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Filippov V.V., “Partial mappings, Čech homology and ordinary differential equations”, Topology Appl., 221 (2017), 647–655
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