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Mat. Sb., 1994, Volume 185, Number 11, Pages 95–118 (Mi msb942)  

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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English version:
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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\by V.~V.~Filippov
\paper On the theory of the Cauchy problem for an~ordinary differential equation with discontinuous right-hand side
\jour Mat. Sb.
\yr 1994
\vol 185
\issue 11
\pages 95--118
\mathnet{http://mi.mathnet.ru/msb942}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1310981}
\zmath{https://zbmath.org/?q=an:0841.34001|0837.34009}
\transl
\jour Russian Acad. Sci. Sb. Math.
\yr 1995
\vol 83
\issue 2
\pages 383--403
\crossref{https://doi.org/10.1070/SM1995v083n02ABEH003597}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1995TQ10300007}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Filippov V., “Differential-Inclusions of 2nd-Order - Cauchy-Problem, Periodic-Solutions”, Dokl. Akad. Nauk, 344:3 (1995), 311–314  mathnet  mathscinet  zmath  isi
    2. V. V. Filippov, “Existence of periodic solutions”, Math. Notes, 61:5 (1997), 644–656  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. 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  mathnet  mathscinet  zmath  isi
    4. Filippov A., “Stability and Instability by the First Approximation”, Differ. Equ., 36:4 (2000), 529–539  mathnet  crossref  mathscinet  zmath  isi
    5. V. V. Filippov, “Optimal Solution Space and Regularization of Equations with Discontinuities in the Space Variables”, Math. Notes, 70:3 (2001), 413–421  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    6. 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  mathnet  crossref  mathscinet  zmath  isi  elib
    7. V. V. Filippov, “On the existence of periodic solutions of equations with strongly increasing principal part”, Sb. Math., 193:11 (2002), 1707–1729  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    8. Filippov V., “On a Scalar Equation with Discontinuous Right-Hand Side and the Uniqueness Theorem”, Differ. Equ., 38:10 (2002), 1435–1445  mathnet  crossref  mathscinet  zmath  isi
    9. A. V. Zuev, “On periodic solutions of ordinary differential equations with discontinuous right-hand side”, Math. Notes, 79:4 (2006), 518–527  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    10. D. A. Serkov, “Minimizatsiya riska pri funktsionalnykh ogranicheniyakh na dinamicheskuyu pomekhu”, Izv. IMI UdGU, 2014, no. 2(44), 3–95  mathnet
    11. Filippov V.V., “Partial mappings, Čech homology and ordinary differential equations”, Topology Appl., 221 (2017), 647–655  crossref  mathscinet  zmath  isi  scopus
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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