Periodic Solutions of Scalar Differential Equations without Uniqueness
Bollettino della Unione matematica italiana, Série 9, Tome 2 (2009) no. 2, pp. 445-448.

Voir la notice de l'article provenant de la source Biblioteca Digitale Italiana di Matematica

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.
@article{BUMI_2009_9_2_2_a8,
     author = {S\c{e}dziwy, Stanis{\l}aw},
     title = {Periodic {Solutions} of {Scalar} {Differential} {Equations} without {Uniqueness}},
     journal = {Bollettino della Unione matematica italiana},
     pages = {445--448},
     publisher = {mathdoc},
     volume = {Ser. 9, 2},
     number = {2},
     year = {2009},
     zbl = {1178.34045},
     mrnumber = {2537280},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BUMI_2009_9_2_2_a8/}
}
TY  - JOUR
AU  - Sȩdziwy, Stanisław
TI  - Periodic Solutions of Scalar Differential Equations without Uniqueness
JO  - Bollettino della Unione matematica italiana
PY  - 2009
SP  - 445
EP  - 448
VL  - 2
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/BUMI_2009_9_2_2_a8/
LA  - en
ID  - BUMI_2009_9_2_2_a8
ER  - 
%0 Journal Article
%A Sȩdziwy, Stanisław
%T Periodic Solutions of Scalar Differential Equations without Uniqueness
%J Bollettino della Unione matematica italiana
%D 2009
%P 445-448
%V 2
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/BUMI_2009_9_2_2_a8/
%G en
%F BUMI_2009_9_2_2_a8
Sȩdziwy, Stanisław. Periodic Solutions of Scalar Differential Equations without Uniqueness. Bollettino della Unione matematica italiana, Série 9, Tome 2 (2009) no. 2, pp. 445-448. http://geodesic.mathdoc.fr/item/BUMI_2009_9_2_2_a8/

[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. | DOI | MR

[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. | DOI | MR | Zbl

[3] J. Andres - K. Pastor, A version of Sharkovskii Theorem for differential equations, Proceedings of the AMS, 133 (2005), 449-453. | DOI | MR | Zbl

[4] E. A. Coddington - N. Levinson, Theory of Ordinary Differential Equations, McGraw-Hill (New York, Toronto, London, 1955). | MR | Zbl

[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

[6] T. Y. Li - J. A. Jorke, Period three implies chaos, American Mathematical Monthly, 82 (1975), 985-992. | DOI | MR | Zbl

[7] F. Obersnel - P. Omari, Period two implies chaos for a class of ODEs, Proceedings of the AMS, 135 (2007), 2055-2058. | DOI | MR | Zbl

[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. | DOI | MR | Zbl