Book Review
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MathSciNet review:
1568171
Full text of review:
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This review is available free of charge.
Book Information:
Author:
Klaus Deimling
Title:
Multivalued differential equations
Additional book information:
de Gruyter, Berlin and New York, 1992, 260 pp., US$59.00. ISBN 3-11-0132125.
H. A. Antosiewicz and A. Cellina, Continuous selections and differential relations, J. Differential Equations 19 (1975), no. 2, 386–398. MR 430368, DOI 10.1016/0022-0396(75)90011-X
Jean-Pierre Aubin, Viability theory, Systems & Control: Foundations & Applications, Birkhäuser Boston, Inc., Boston, MA, 1991. MR 1134779
Jean-Pierre Aubin and Arrigo Cellina, Differential inclusions, Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 264, Springer-Verlag, Berlin, 1984. Set-valued maps and viability theory. MR 755330, DOI 10.1007/978-3-642-69512-4
Alberto Bressan, Directionally continuous selections and differential inclusions, Funkcial. Ekvac. 31 (1988), no. 3, 459–470. MR 987798
Arrigo Cellina, Multivalued differential equations and ordinary differential equations, SIAM J. Appl. Math. 18 (1970), 533–538. MR 276537, DOI 10.1137/0118046
F. S. De Blasi and G. Pianigiani, A Baire category approach to the existence of solutions of multivalued differential equations in Banach spaces, Funkcial. Ekvac. 25 (1982), no. 2, 153–162. MR 694909
F. S. De Blasi and G. Pianigiani, The Baire category method in existence problems for a class of multivalued differential equations with nonconvex right-hand side, Funkcial. Ekvac. 28 (1985), no. 2, 139–156. MR 816823
A. F. Filippov, On certain questions in the theory of optimal control, J. SIAM Control Ser. A 1 (1962), 76–84. MR 0149985
A. F. Filippov, The existence of solutions of multivalued differential equations, Mat. Zametki 10 (1971), 307–313 (Russian). MR 298090
[10] -, Differential equations with discontinuous right-hand sides, Kluwer, Dordrecht, 1988.
Andrzej Fryszkowski, Continuous selections for a class of nonconvex multivalued maps, Studia Math. 76 (1983), no. 2, 163–174. MR 730018, DOI 10.4064/sm-76-2-163-174
MichałKisielewicz, Differential inclusions and optimal control, Mathematics and its Applications (East European Series), vol. 44, Kluwer Academic Publishers Group, Dordrecht; PWN—Polish Scientific Publishers, Warsaw, 1991. MR 1135796
- [1]
- H. Antosiewicz and A. Cellina, Continuous selections and differential relations, J. Differential Equations 19 (1975), 386-398. MR 0430368 (55:3373)
- [2]
- J. P. Aubin, Viability theory, Birkhäuser, Basel and Boston, MA, 1992. MR 1134779 (92k:49003)
- [3]
- J. P. Aubin and A. Cellina, Differential inclusions, Springer, New York, 1984. MR 755330 (85j:49010)
- [4]
- A. Bressan, Directionally continuous selections and differential inclusions, Funkcial. Ekvac. 31 (1988), 459-470. MR 987798 (90d:34038)
- [5]
- A. Cellina, Multivalued differential equations and ordinary differential equations, SIAM J. Appl. Math. 18 (1970), 553-558. MR 0276537 (43:2281)
- [6]
- F. De Blasi and G. Pianigiani, A Baire category approach to the existence of solutions of multivalued differential equations in Banach spaces, Funkcial Ekvac. 25 (1982), 153-162. MR 694909 (84e:34019)
- [7]
- -, The Baire category method in existence problems for a class of multivalued differential equations with nonconvex right hand side, Funkcial. Ekvac. 28 (1985), 139-156. MR 816823 (87c:34018)
- [8]
- A. F. Filippov, On certain questions in the theory of optimal control, SIAM J. Control Optim. 1 (1962), 76-84. MR 0149985 (26:7469)
- [9]
- -, On the existence of solutions of multivalued differential equations, Mat. Zametki 10 (1971), 307-313. MR 0298090 (45:7142)
- [10]
- -, Differential equations with discontinuous right-hand sides, Kluwer, Dordrecht, 1988.
- [11]
- A. Fryskowski, Continuous selections for a class of nonconvex multivalued maps, Studia Math. 76 (1983), 163-174. MR 730018 (85j:54022)
- [12]
- M. Kisielewicz, Differential inclusions and optimal control, PWN, Warsaw, 1991. MR 1135796 (93c:49001)
Review Information:
Reviewer:
Arrigo Cellina
Journal:
Bull. Amer. Math. Soc.
32 (1995), 275-278
DOI:
https://doi.org/10.1090/S0273-0979-1995-00575-6
