|
Isolating segments for Carathéodory systems and existence of periodic solutions
Author(s):
Maciej
J.
Capinski;
Klaudiusz
Wójcik
Journal:
Proc. Amer. Math. Soc.
131
(2003),
2443-2451.
MSC (2000):
Primary 34A26, 34B15
Posted:
November 13, 2002
Retrieve article in:
PDF DVI PostScript
Abstract |
References |
Similar articles |
Additional information
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:
- [A]
- J. Andres ``A nontrivial example of application of the Nielsen fixed-point theory to differential systems: problem of Jean Leray" Proc. AMS (2000) vol. 128, 2921-2931. MR 2000m:47074
- [AGJ]
- 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.
- [AG]
- J. Andres, L. Górniewicz ``From the Schauder Fixed-Point Theorem to The Applied Multivalued Nielsen Theory" TMNA vol. 14, (1999), 229-238. MR 2001h:47092
- [F]
- H. Federer ``Geometric measure theory". Die Grundlehren der mathematischen Wissenschaften, Band 153 Springer-Verlag New York Inc., New York, 1969. MR 41:1976
- [G]
- A. Granas ``The Leray-Schauder index and the fixed point theory for arbitrary ANR's" Bull. Soc. Math. France 100 (1972), 209-228. MR 46:8213
- [H]
- P. Hartman ``Ordinary Differential Equations" John Wiley, New York, 1964. MR 30:1270
- [N]
- S. Nakagiri, H. Murakami ``Kneser's property of solutions families of nonlinear Volterra integral equations" Proc. Japan Acad. 50 (1974), 296-300. MR 50:14138
- [S]
- R. Srzednicki ``Periodic and bounded solutions in blocks for time-periodic nonautonomous ODE's" Nonlinear Anal. TMA 22 (1994), 707-737. MR 95c:34076
Similar Articles:
Retrieve articles in Proceedings of the American Mathematical Society
with MSC
(2000):
34A26, 34B15
Retrieve articles in all Journals with MSC
(2000):
34A26, 34B15
Additional Information:
Maciej
J.
Capinski
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
DOI:
10.1090/S0002-9939-02-06801-6
PII:
S 0002-9939(02)06801-6
Keywords:
Carath\'eodory systems,
periodic solutions,
isolating segments
Received by editor(s):
December 11, 2001
Received by editor(s) in revised form:
March 13, 2002
Posted:
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 of article:
Copyright
2002,
American Mathematical Society
|
Comments: webmaster@ams.org