On the properties of the Aumann integral with applications to differential inclusions and control systems

 Access to full text

 Full (PDF)

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. (1980) MR0564562
2. Z. Artstein J. Burns, Integration of compact set valued functions, Pacific J. Math. 58 (1975) pp.297-307. (1975) MR0385061
3. R. Aumann, 10.1016/0022-247X(65)90049-1, J. Math. Anal. Appl. 12 (1965) pp. 1-12. (1965) MR0185073DOI10.1016/0022-247X(65)90049-1
4. M. Benamara, Sections measurables extrémales d'une multiapplication, C.R. Acad. Sc. Paris t. 278 (1974) pp. 1249-1252. (1974) MR0352982
5. M. Benamara, Points extremaux, multiapplications et fonctionelles integrales, Thése de cycle, Université de Grenoble (1975). (1975) 
6. V. Blagodatskikh, Convexity of attainability spheres, Diff. Eq. 8 (1972) pp. 1661-1665. (1972) 
7. C. Castaing M. Valadier, 10.1007/BFb0087688, Lecture Notes in Math. Vol. 580, Springer, Berlin (1977). (1977) MR0467310DOI10.1007/BFb0087688
8. A. Cellina, On the differential inclusion $x\in [-1,1]$, Rend. Acad. Naz. Lincei 69 (1980) pp. 1-6. (1980) MR0641583
9. L. Cesari, 10.1137/0313037, S.T.A.M. J. Contr. Optim. 13 (1975) pp. 666-676. (1975) Zbl0295.28016MR0380595DOI10.1137/0313037
10. F. Clarke, Optimization and Nonsmooth Analysis, Wiley, New York (1983). (1983) Zbl0582.49001MR0709590
11. E. Cramer V. Laksmikantham A. Mitchell, 10.1016/0362-546X(78)90063-9, Nonl. Anal. T.M.A. 2 (1978) pp. 169- 177. (1978) MR0512280DOI10.1016/0362-546X(78)90063-9
12. R. Datko, 10.1016/0022-247X(65)90123-X, J. Math. Anal. Appl. 10 (1965) pp. 284-194. (1965) Zbl0131.05301MR0174419DOI10.1016/0022-247X(65)90123-X
13. R. Datko, 10.4064/fm-78-3-205-208, Fund. Math. 78 (1973) pp. 205-208. (1973) MR0374372DOI10.4064/fm-78-3-205-208
14. J. L. Davy, 10.1017/S0004972700044646, Bull. Austr. Math. Soc. 6 (1972) pp. 379-298. (1972) Zbl0239.49022MR0303023DOI10.1017/S0004972700044646
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. (1985) MR0694909
16. F. DeBlasi G. Pianigiani, Remark on Hausdorff continuous multifunctions and selections, Comm. Math. Univ. Carolinae 24 (1983) pp. 553-562. (1983) MR0730150
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. (1967) Zbl0211.52803MR0228252
18. J. Diestel J. Uhl, Vector Measures, Math. Surveys, Vol. 15, A.M.S., Providence (1977). (1977) MR0453964
19. J. Dugundji, Topology, Allyn and Bacon Inc., Boston (1966). (1966) Zbl0144.21501MR0193606
20. F. Hiai H. Umegaki, 10.1016/0047-259X(77)90037-9, J. Multiv. Anal. 7 (1977) pp. 149-182. (1977) MR0507504DOI10.1016/0047-259X(77)90037-9
21. C. Himmelberg, 10.4064/fm-87-1-53-72, Fund. Math. 87 (1975) pp. 53 - 72. (1975) Zbl0296.28003MR0367142DOI10.4064/fm-87-1-53-72
22. K. Grasse, 10.1007/BF00933938, J. Optim. The. Appl. 40 (1983) pp. 221-35. (1983) Zbl0488.49006MR0703317DOI10.1007/BF00933938
23. J. Jarník J. Kurzweil, Integral of multivalued mappings and its connection with differential relations, Časopis pro pěstování matematiky 108 (1983) pp. 8-28. (1983) MR0694137
24. N. Kikuchi, 10.2977/prims/1195195563, Publ. R.I.M.S. Kyoto Univ 3 (1966), pp. 177-201. (1966) MR0227580DOI10.2977/prims/1195195563
25. I. Kluvánek G. Knowles, Vector Measures and Control Systems, Math. Studies, Vol. 20, North Holland, Amsterdam (1975). (1975) MR0499068
26. J. Kurzweil, Generalized ordinary differential equations and continuous dependence on a parameter, Czechoslovak Math. J. 7 (82) (1957), pp. 418-449. (1957) Zbl0090.30002MR0111875
27. J. Kurzweil, Generalized ordinary differential equations, Czechoslovak Math. J. 8 (83) (1958), pp. 360-388. (1958) Zbl0102.07003MR0111878
28. N. S. Papageorgiou, 10.1016/0047-259X(85)90078-8, J. Multiv. Anal. 17 (1985), pp. 185-207. (1985) DOI10.1016/0047-259X(85)90078-8
29. N. S. Papageorgiou, 10.1090/S0002-9947-1985-0808737-3, Trans. Amer. Math. Soc. 292 (1985), pp. 557-572. (1985) Zbl0605.46037MR0808737DOI10.1090/S0002-9947-1985-0808737-3
30. N. S. Papageorgiou, 10.1016/0022-247X(86)90339-2, J. Math. Anal. Appl. 113 (1986), pp. 148-163. (1986) Zbl0603.28010MR0826665DOI10.1016/0022-247X(86)90339-2
31. N. S. Papageorgiou, 10.1016/0022-0396(86)90021-5, J. Diff. Eq. 65 (1986), pp.287-303. (1986) Zbl0615.34006MR0865064DOI10.1016/0022-0396(86)90021-5
32. R. T. Rockafellar, 10.1007/BFb0079944, Lecture Notes in Math. Vol. 543, Springer, Berlin (1976), pp. 157-207. (1976) Zbl0374.49001MR0512209DOI10.1007/BFb0079944
33. G. Stefani P. Zecca, 10.1215/ijm/1256047473, Illinois J. Math. 24 (1980), pp. 560-575. (1980) MR0586796DOI10.1215/ijm/1256047473
34. H. Tanabe, Equations of Evolution, Pitman, London (1979). (1979) Zbl0417.35003MR0533824
35. D. Wagner, 10.1137/0315056, S.I.A.M. J. Conti. Optim. 15 (1977), pp. 859-903. (1977) Zbl0407.28006MR0486391DOI10.1137/0315056

1. Dimitrios A. Kandilakis, Nikolaos S. Papageorgiou, Correction on “The properties of the Aumann integral with applications to differential inclusions and control systems”
2. Nikolaos S. Papageorgiou, On nonconvex valued Volterra integral inclusions in Banach spaces
3. Nikolaos S. Papageorgiou, Existence of solutions for integrodifferential inclusions in Banach spaces
4. Nikolaos S. Papageorgiou, On integral inclusions of Volterra type in Banach spaces
5. Nikolaos S. Papageorgiou, Convexity of the orientor field and the solution set of a class of evolution inclusions