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An application of the Lefschetz fixed-point theorem to non-convex differential inclusions on manifolds
Author(s):
Stanislaw
Domachowski;
Tadeusz
Pruszko
Journal:
Proc. Amer. Math. Soc.
126
(1998),
1231-1236.
MSC (1991):
Primary 58F32;
Secondary 47H04, 28B20
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Abstract:
A selector theorem for non-convex orientor fields on closed manifolds is given and the Lefschetz fixed point theorem is used to establish an existence result for these ones.
References:
- [1]
- H.A. Antosiewicz and A. Cellina, Continuous selections and differential relations, J. Differential Equations, 19 (1975), pp. 386 - 398. MR 55:3373
- [2]
- A. Bressan and G. Colombo, Extensions and selections of maps with decomposable values, Studia Math., 90 (1988), pp. 70 - 85. MR 89j:54021
- [3]
- S. Domachowski and T. Pruszko, An application of the Eilenberg - Montgomery theorem to measurable orientor fields on manifolds, Funkcialaj Ekvacioj, 36 (1993), pp. 95 - 107. MR 94e:58008
- [4]
- A.F. Filippov, The existence of solutions of multivalued differential equations (in Russian), Mat. Zametki, 10 (1971), pp. 307 - 313. MR 45:7142
- [5]
- A. Fryszkowski, Continuous selections for a class of non-convex multivalued maps, Studia Math., 76 (1983), 163 - 174. MR 85j:54022
- [6]
- A. Granas, Points fixes pour les applications compactes: espaces de Lefschetz et théorie de l'indice, Notes de cours, Séminaire de Mathematiques Supérieurs, Montréal, 1973. [Les Press de l'Université de Montréal, 1980.] MR 81i:55002
- [7]
- H. Kaczy\'{n}ski and C. Olech, Existence of solutions of orientor fields with non-convex right-hand side, Ann. Polon. Math. 29 (1974), pp. 61 - 66. MR 50:10974
- [8]
- S. {\L}ojasiewicz (Jr), The existence of solutions for lower semicontinuous orientor fields, Bull. Acad. Polon. Sci., 28, no. 9-10 (1980), pp. 483-487. MR 82j:34013
- [9]
- C. Olech, Existence of solutions of non-convex orientor fields, Bull Unione Math. Ital., 11 (1975), pp. 189 - 197. MR 52:15174
- [10]
- T. Pruszko, Some applications of the topological degree theory to multivalued boundary value problems, Dissertationes Math. 229 (1984). MR 85j:34030
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Additional Information:
Stanislaw
Domachowski
Affiliation:
Institute of Mathematics, Gdansk University, ul. Wita Stwosza 57, 80--952 Gdansk, Poland
Tadeusz
Pruszko
Affiliation:
Institute of Mathematics, Gdansk University, ul. Wita Stwosza 57, 80--952 Gdansk, Poland
DOI:
10.1090/S0002-9939-98-04278-6
PII:
S 0002-9939(98)04278-6
Received by editor(s):
September 23, 1996
Additional Notes:
The work of the first author was supported by the University of Gdansk, grant nr BW-5100-5-0055-6
Communicated by:
Hal L. Smith
Copyright of article:
Copyright
1998,
American Mathematical Society
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