Abstract:
This article gives an approach to the study of both differential inclusions and ordinary differential equations in a Banach space X. The central point concerns the question of the existence and properties of the solution set of a differential inclusion whose right-hand side has the weak Scorza–Dragoni property.
Bibliography: 37 titles.
Citation:
A. A. Tolstonogov, I. A. Finogenko, “On solutions of a differential inclusion with lower semicontinuous nonconvex right-hand side in a Banach space”, Math. USSR-Sb., 53:1 (1986), 203–231
\Bibitem{TolFin84}
\by A.~A.~Tolstonogov, I.~A.~Finogenko
\paper On solutions of a~differential inclusion with lower semicontinuous nonconvex right-hand side in a~Banach space
\jour Math. USSR-Sb.
\yr 1986
\vol 53
\issue 1
\pages 203--231
\mathnet{http://mi.mathnet.ru/eng/sm2079}
\crossref{https://doi.org/10.1070/SM1986v053n01ABEH002917}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=764478}
\zmath{https://zbmath.org/?q=an:0588.34012}
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https://doi.org/10.1070/SM1986v053n01ABEH002917
https://www.mathnet.ru/eng/sm/v167/i2/p199
This publication is cited in the following 16 articles:
Hamza El-Kebir, Ani Pirosmanishvili, Melkior Ornik, “Online Guaranteed Reachable Set Approximation for Systems With Changed Dynamics and Control Authority”, IEEE Trans. Automat. Contr., 69:2 (2024), 726
I. A. Finogenko, “Limit differential inclusions and the invariance principle for nonautonomous systems”, Siberian Math. J., 55:2 (2014), 372–386
Bulgakov A.I., Skomorokhov V.V., Filippova O.V., “Approksimatsiya funktsionalno-differentsialnogo vklyucheniya s impulsnymi vozdeistviyami i vnutrennimi i vneshnimi vozmuscheniyami”, Vestnik tambovskogo universiteta. seriya: estestvennye i tekhnicheskie nauki, 17:1 (2012), 32–37
Approximation of functional-differential inclusion with impulses and with internal and external perturbations
I. A. Finogenko, “On differential inclusions with additive generalized functions”, Proc. Steklov Inst. Math. (Suppl.), 271, suppl. 1 (2010), S85–S94
A. I. Bulgakov, O. P. Belyaeva, A. A. Grigorenko, “On the theory of perturbed inclusions and its applications”, Sb. Math., 196:10 (2005), 1421–1472
Condensing Multivalued Maps and Semilinear Differential Inclusions in Banach Spaces, 2001, 213
Mikhail Kamenskii, Valeri Obukhovskii, Pietro Zecca, “On semilinear differential inclusions with lower semicontinuous nonlinearities”, Annali di Matematica, 178:1 (2000), 235
A. I. Bulgakov, L. I. Tkach, “Perturbation of a convex-valued operator by a set-valued map of Hammerstein type with non-convex values, and boundary-value problems for functional-differential inclusions”, Sb. Math., 189:6 (1998), 821–848
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A. I. Bulgakov, “Integral inclusions with nonconvex images, and their applications to boundary value problems for differential inclusions”, Russian Acad. Sci. Sb. Math., 77:1 (1994), 193–212
Bulgakov A., “Continuous Branches of Multivalued Functions and Integral Inclusions with Nonconvex Ranges and their Applications .3.”, Differ. Equ., 28:5 (1992), 587–592
Multivalued Differential Equations, 1992, 243
S. I. Suslov, “The nonlinear bang-bang principle in a Banach space”, Siberian Math. J., 33:4 (1992), 675–685
F.S De Blasi, G Pianigiani, “Non-convex-valued differential inclusions in Banach spaces”, Journal of Mathematical Analysis and Applications, 157:2 (1991), 469
Giulio Pianigiani, Lecture Notes in Mathematics, 1446, Methods of Nonconvex Analysis, 1990, 104
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