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 Tr. Mat. Inst. Steklova, 2013, Volume 283, Pages 121–141 (Mi tm3505)

Differential inclusions with measurable-pseudo-Lipschitz right-hand side

E. S. Polovinkin

Moscow Institute of Physics and Technology (State University), Dolgoprudny, Moscow region, Russia

Abstract: We obtain existence theorems and Filippov–Ważewski type relaxation theorems for differential inclusions in Banach spaces with measurable-pseudo-Lipschitz right-hand side. For the solution sets of these differential inclusions, we also describe some properties that extend classical theorems on continuous dependence and on differentiation of solutions with respect to initial data.

DOI: https://doi.org/10.1134/S0371968513040092

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English version:
Proceedings of the Steklov Institute of Mathematics, 2013, 283, 116–135

Bibliographic databases:

UDC: 517.9

Citation: E. S. Polovinkin, “Differential inclusions with measurable-pseudo-Lipschitz right-hand side”, Function theory and equations of mathematical physics, Collected papers. In commemoration of the 90th anniversary of Lev Dmitrievich Kudryavtsev's birth, Tr. Mat. Inst. Steklova, 283, MAIK Nauka/Interperiodica, Moscow, 2013, 121–141; Proc. Steklov Inst. Math., 283 (2013), 116–135

Citation in format AMSBIB
\Bibitem{Pol13} \by E.~S.~Polovinkin \paper Differential inclusions with measurable-pseudo-Lipschitz right-hand side \inbook Function theory and equations of mathematical physics \bookinfo Collected papers. In commemoration of the 90th anniversary of Lev Dmitrievich Kudryavtsev's birth \serial Tr. Mat. Inst. Steklova \yr 2013 \vol 283 \pages 121--141 \publ MAIK Nauka/Interperiodica \publaddr Moscow \mathnet{http://mi.mathnet.ru/tm3505} \crossref{https://doi.org/10.1134/S0371968513040092} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3479952} \elib{http://elibrary.ru/item.asp?id=20783234} \transl \jour Proc. Steklov Inst. Math. \yr 2013 \vol 283 \pages 116--135 \crossref{https://doi.org/10.1134/S0081543813080099} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000330983000008} \elib{http://elibrary.ru/item.asp?id=35475052} 

• http://mi.mathnet.ru/eng/tm3505
• https://doi.org/10.1134/S0371968513040092
• http://mi.mathnet.ru/eng/tm/v283/p121

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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. E. S. Polovinkin, “Subdifferentials for the difference of two convex functions”, J. Math. Sci., 218:5 (2016), 664–677
2. E. S. Polovinkin, “Differential inclusions with unbounded right-hand side and necessary optimality conditions”, Proc. Steklov Inst. Math., 291 (2015), 237–252
3. E. S. Polovinkin, “Calculation of subdifferentials for the difference of two convex functions”, J. Convex Anal., 24:1 (2017), 287–303
4. E. S. Polovinkin, “Calculation of subdifferentials for the difference of two convex functions”, 2017 Constructive Nonsmooth Analysis and Related Topics (Dedicated to the Memory of V. F. Demyanov) (CNSA), ed. L. Polyakova, IEEE, 2017, 261–262
5. E. S. Polovinkin, “Necessary optimality conditions for the Mayer problem with unbounded differential inclusion”, IFAC PAPERSONLINE, 51:32 (2018), 521–524
6. E. S. Polovinkin, “O nepreryvnoi zavisimosti traektorii differentsialnogo vklyucheniya ot nachalnykh priblizhenii”, Tr. IMM UrO RAN, 25, no. 1, 2019, 174–195
7. E. S. Polovinkin, “Pontryagin's Direct Method for Optimization Problems with Differential Inclusion”, Proc. Steklov Inst. Math., 304 (2019), 241–256
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