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Sȩdziwy, Stanisław:
Periodic Solutions of Scalar Differential Equations without Uniqueness
Bollettino dell'Unione Matematica Italiana Serie 9 2 (2009), fasc. n.2, p. 445-448, (English)
pdf (84 Kb), djvu (50 Kb). | MR 2537280 | Zbl 1178.34045

Sunto

The note presents a simple proof of a result due to F. Obersnel and P. Omari on the existence of periodic solutions with an arbitrary period of the first order scalar differential equation, provided equation has an n-periodic solution with the minimal period n > 1.
Referenze Bibliografiche
[1] J. ANDRES - J. FIŠER - L. JÜTTNER, On a multivalued version of the Sharkovskii Theorem and its application to differential inclusions, Set-Valued Analysis, 10 (2002), 1-14. | fulltext (doi) | MR 1888453
[2] J. ANDRES - T. FÜRST - K. PASTOR, Period two implies all periods for a class of ODEs: A multivalued map approach, Proceedings of the AMS, 135 (2007), 3187-3191. | fulltext (doi) | MR 2322749 | Zbl 1147.34031
[3] J. ANDRES - K. PASTOR, A version of Sharkovskii Theorem for differential equations, Proceedings of the AMS, 133 (2005), 449-453. | fulltext (doi) | MR 2093067 | Zbl 1063.34030
[4] E. A. CODDINGTON - N. LEVINSON, Theory of Ordinary Differential Equations, McGraw-Hill (New York, Toronto, London, 1955). | MR 69338 | Zbl 0064.33002
[5] R. DEVANEY - S. SMALE - M. W. HIRSCH, Differential Equations, Dynamical Systems, and an Introduction to Chaos, Ed. 2 Acad. Press (N. York, 2003). | MR 2144536
[6] T. Y. LI - J. A. JORKE, Period three implies chaos, American Mathematical Monthly, 82 (1975), 985-992. | fulltext (doi) | MR 385028 | Zbl 0351.92021
[7] F. OBERSNEL - P. OMARI, Period two implies chaos for a class of ODEs, Proceedings of the AMS, 135 (2007), 2055-2058. | fulltext (doi) | MR 2299480 | Zbl 1124.34335
[8] F. OBERSNEL - P. OMARI, Old and new results for first order periodic ODEs without uniqueness: a comprehensive study by lower and upper solutions, Advanced Non-linear Studies, 4 (2004), 323-376. | fulltext (doi) | MR 2079818 | Zbl 1072.34041

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