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Title: On the properties of the Aumann integral with applications to differential inclusions and control systems (English)
Author: Kandilakis, Dimitrios A.
Author: Papageorgiou, Nikolaos S.
Language: English
Journal: Czechoslovak Mathematical Journal
ISSN: 0011-4642 (print)
ISSN: 1572-9141 (online)
Volume: 39
Issue: 1
Year: 1989
Pages: 1-15
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Category: math
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MSC: 28B20
MSC: 49A27
MSC: 49E10
idZBL: Zbl 0677.28005
idMR: MR983479
DOI: 10.21136/CMJ.1989.102274
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Date available: 2008-06-09T15:24:52Z
Last updated: 2020-07-28
Stable URL: http://hdl.handle.net/10338.dmlcz/102274
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Reference: [1] Z. Artstein: Discrete and continuous bang-bang and facial spaces. Or: look for extreme points.S.I.A.M. Rev. 22 (1980) pp. 172-185. MR 0564562
Reference: [2] Z. Artstein J. Burns: Integration of compact set valued functions.Pacific J. Math. 58 (1975) pp.297-307. MR 0385061
Reference: [3] R. Aumann: Integrals of set valued function.J. Math. Anal. Appl. 12 (1965) pp. 1-12. MR 0185073, 10.1016/0022-247X(65)90049-1
Reference: [4] M. Benamara: Sections measurables extrémales d'une multiapplication.C.R. Acad. Sc. Paris t. 278 (1974) pp. 1249-1252. MR 0352982
Reference: [5] M. Benamara: Points extremaux, multiapplications et fonctionelles integrales.Thése de $3^{eme}$ cycle, Université de Grenoble (1975).
Reference: [6] V. Blagodatskikh: Convexity of attainability spheres.Diff. Eq. 8 (1972) pp. 1661-1665.
Reference: [7] C. Castaing M. Valadier: Convex Analysis and Measurable Multifunctions.Lecture Notes in Math. Vol. 580, Springer, Berlin (1977). MR 0467310, 10.1007/BFb0087688
Reference: [8] A. Cellina: On the differential inclusion $x \in [-1, 1]$.Rend. Acad. Naz. Lincei 69 (1980) pp. 1-6. MR 0641583
Reference: [9] L. Cesari: Convexity of the range of certain integrals.S.T.A.M. J. Contr. Optim. 13 (1975) pp. 666-676. Zbl 0295.28016, MR 0380595, 10.1137/0313037
Reference: [10] F. Clarke: Optimization and Nonsmooth Analysis.Wiley, New York (1983). Zbl 0582.49001, MR 0709590
Reference: [11] E. Cramer V. Laksmikantham A. Mitchell: On the existence of weak solutions of differential equations in nonreflexive Banach spaces.Nonl. Anal. T.M.A. 2 (1978) pp. 169- 177. MR 0512280, 10.1016/0362-546X(78)90063-9
Reference: [12] R. Datko: A general bang-bang principle and bang-bang approximations.J. Math. Anal. Appl. 10 (1965) pp. 284-194. Zbl 0131.05301, MR 0174419, 10.1016/0022-247X(65)90123-X
Reference: [13] R. Datko: On the integration of set valued mappings in Banach spaces.Fund. Math. 78 (1973) pp. 205-208. MR 0374372, 10.4064/fm-78-3-205-208
Reference: [14] J. L. Davy: Properties of the solution set of a generalized differential equation.Bull. Austr. Math. Soc. 6 (1972) pp. 379-298. Zbl 0239.49022, MR 0303023, 10.1017/S0004972700044646
Reference: [15] F. DeBlasi G. Pianigiani: A Baire category approach to the existence of solutions of multivalued differential equations in Banach spaces.Funkc. Ekvac. 25 (1985) pp. 153-162. MR 0694909
Reference: [16] F. DeBlasi G. Pianigiani: Remark on Hausdorff continuous multifunctions and selections.Comm. Math. Univ. Carolinae 24 (1983) pp. 553-562. MR 0730150
Reference: [17] G. Debreu: Integration of correspondences.Proc. of 5th Berkeley Symp. Math. Stat. and Probability I, Univ. of Calif. Press, Berkeley (1967) pp. 351-372. Zbl 0211.52803, MR 0228252
Reference: [18] J. Diestel J. Uhl: Vector Measures.Math. Surveys, Vol. 15, A.M.S., Providence (1977). MR 0453964
Reference: [19] J. Dugundji: Topology.Allyn and Bacon Inc., Boston (1966). Zbl 0144.21501, MR 0193606
Reference: [20] F. Hiai H. Umegaki: Integrals, conditional expectations and martingales of multivalued functions.J. Multiv. Anal. 7 (1977) pp. 149-182. MR 0507504, 10.1016/0047-259X(77)90037-9
Reference: [21] C. Himmelberg: Measurable relations.Fund. Math. 87 (1975) pp. 53 - 72. Zbl 0296.28003, MR 0367142, 10.4064/fm-87-1-53-72
Reference: [22] K. Grasse: Some remarks on extremal solutions of multivalued differential equations.J. Optim. The. Appl. 40 (1983) pp. 221-35. Zbl 0488.49006, MR 0703317, 10.1007/BF00933938
Reference: [23] J. Jarník J. Kurzweil: Integral of multivalued mappings and its connection with differential relations.Časopis pro pěstování matematiky 108 (1983) pp. 8-28. MR 0694137
Reference: [24] N. Kikuchi: On some fundamental theorems of contigent equations in connection with control problems.Publ. R.I.M.S. Kyoto Univ 3 (1966), pp. 177-201. MR 0227580, 10.2977/prims/1195195563
Reference: [25] I. Kluvánek G. Knowles: Vector Measures and Control Systems.Math. Studies, Vol. 20, North Holland, Amsterdam (1975). MR 0499068
Reference: [26] J. Kurzweil: Generalized ordinary differential equations and continuous dependence on a parameter.Czechoslovak Math. J. 7 (82) (1957), pp. 418-449. Zbl 0090.30002, MR 0111875
Reference: [27] J. Kurzweil: Generalized ordinary differential equations.Czechoslovak Math. J. 8 (83) (1958), pp. 360-388. Zbl 0102.07003, MR 0111878
Reference: [28] N. S. Papageorgiou: On the theory of Banach space valued multifunctions. Part 1 : Integration and conditional expectation.J. Multiv. Anal. 17 (1985), pp. 185-207. 10.1016/0047-259X(85)90078-8
Reference: [29] N. S. Papageorgiou: Representation of set valued operators.Trans. Amer. Math. Soc. 292 (1985), pp. 557-572. Zbl 0605.46037, MR 0808737, 10.1090/S0002-9947-1985-0808737-3
Reference: [30] N. S. Papageorgiou: Integral functionals on Souslin locally convex spaces.J. Math. Anal. Appl. 113 (1986), pp. 148-163. Zbl 0603.28010, MR 0826665, 10.1016/0022-247X(86)90339-2
Reference: [31] N. S. Papageorgiou: Random differential inclusions in Banach spaces.J. Diff. Eq. 65 (1986), pp.287-303. Zbl 0615.34006, MR 0865064, 10.1016/0022-0396(86)90021-5
Reference: [32] R. T. Rockafellar: Integral functionals, normal integrands and measurable selections.Lecture Notes in Math. Vol. 543, Springer, Berlin (1976), pp. 157-207. Zbl 0374.49001, MR 0512209, 10.1007/BFb0079944
Reference: [33] G. Stefani P. Zecca: Multivalued differential equations on manifolds with applications to control theory.Illinois J. Math. 24 (1980), pp. 560-575. MR 0586796, 10.1215/ijm/1256047473
Reference: [34] H. Tanabe: Equations of Evolution.Pitman, London (1979). Zbl 0417.35003, MR 0533824
Reference: [35] D. Wagner: Survey of measurable selection theorems.S.I.A.M. J. Conti. Optim. 15 (1977), pp. 859-903. Zbl 0407.28006, MR 0486391, 10.1137/0315056
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