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An application of the Lefschetz fixed-point theorem to non-convex
differential inclusions on manifolds


Authors: Stanislaw Domachowski and Tadeusz Pruszko
Journal: Proc. Amer. Math. Soc. 126 (1998), 1231-1236
MSC (1991): Primary 58F32; Secondary 47H04, 28B20
DOI: https://doi.org/10.1090/S0002-9939-98-04278-6
MathSciNet review: 1443380
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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.


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  • [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, Gdańsk University, ul. Wita Stwosza 57, 80–952 Gdańsk, Poland

Tadeusz Pruszko
Affiliation: Institute of Mathematics, Gdańsk University, ul. Wita Stwosza 57, 80–952 Gdańsk, Poland

DOI: https://doi.org/10.1090/S0002-9939-98-04278-6
Received by editor(s): September 23, 1996
Additional Notes: The work of the first author was supported by the University of Gdańsk, grant nr BW-5100-5-0055-6
Communicated by: Hal L. Smith
Article copyright: © Copyright 1998 American Mathematical Society

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