Isolating segments for Carathéodory systems and existence of periodic solutions
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- by Maciej J. Capiński and Klaudiusz Wójcik
- Proc. Amer. Math. Soc. 131 (2003), 2443-2451
- DOI: https://doi.org/10.1090/S0002-9939-02-06801-6
- Published electronically: November 13, 2002
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Abstract:
The method of isolating segments is introduced in the context of Carathéodory systems. We define isolating segments and extend the results of Srzednicki (1994) to Carathéodory systems.References
- Jan Andres, A nontrivial example of application of the Nielsen fixed-point theory to differential systems: problem of Jean Leray, Proc. Amer. Math. Soc. 128 (2000), no. 10, 2921–2931. MR 1664285, DOI 10.1090/S0002-9939-00-05324-7
- J. Andres, L. Górniewicz, J. Jezierski “Noncompact version of the multivalued Nielsen theory and its application to differential inclusions" Differential Inclusions and Optimal Control, Lecture Notes in Nonlinear Analysis, vol. 2, (1998), 33-50.
- Jan Andres and Lech Górniewicz, From the Schauder fixed-point theorem to the applied multivalued Nielsen theory, Topol. Methods Nonlinear Anal. 14 (1999), no. 2, 229–238. MR 1766189, DOI 10.12775/TMNA.1999.030
- Herbert Federer, Geometric measure theory, Die Grundlehren der mathematischen Wissenschaften, Band 153, Springer-Verlag New York, Inc., New York, 1969. MR 0257325
- Andrzej Granas, The Leray-Schauder index and the fixed point theory for arbitrary ANRs, Bull. Soc. Math. France 100 (1972), 209–228. MR 309102
- Philip Hartman, Ordinary differential equations, John Wiley & Sons, Inc., New York-London-Sydney, 1964. MR 0171038
- Shinichi Nakagiri and Haruo Murakami, Kneser’s property of solution families of non-linear Volterra integral equations, Proc. Japan Acad. 50 (1974), 296–300. MR 361693
- Roman Srzednicki, Periodic and bounded solutions in blocks for time-periodic nonautonomous ordinary differential equations, Nonlinear Anal. 22 (1994), no. 6, 707–737. MR 1270166, DOI 10.1016/0362-546X(94)90223-2
Bibliographic Information
- Maciej J. Capiński
- Affiliation: Institute of Mathematics, Jagiellonian University, Reymonta 4, 30-059 Kraków, Poland
- Email: mcapinsk@im.uj.edu.pl
- Klaudiusz Wójcik
- Affiliation: Institute of Mathematics, Jagiellonian University, Reymonta 4, 30-059 Kraków, Poland
- Email: wojcik@im.uj.edu.pl
- Received by editor(s): December 11, 2001
- Received by editor(s) in revised form: March 13, 2002
- Published electronically: November 13, 2002
- Additional Notes: The second author was partially supported by Polish KBN grant 2 P 03A 028 17.
- Communicated by: Carmen C. Chicone
- © Copyright 2002 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 131 (2003), 2443-2451
- MSC (2000): Primary 34A26, 34B15
- DOI: https://doi.org/10.1090/S0002-9939-02-06801-6
- MathSciNet review: 1974642