Email this article The least distance between extremums and minimal period of solutions to autonomous vector differential equations
- Authors: Zevin A.A.1
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Affiliations:
- ITST NAS of Ukraine
- Issue: Vol 485, No 2 (2019)
- Pages: 142-144
- Section: Mathematics
- URL: https://journals.eco-vector.com/0869-5652/article/view/12820
- DOI: https://doi.org/10.31857/S0869-56524852142-144
- ID: 12820
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Abstract
Solutions x(t) of the Lipschitz equation x = f(x) with an arbitrary vector norm are considered. It is proved that the sharp lower bound for the distances between successive extremums of xk(t) equals π/L where L is the Lipschitz constant. For non-constant periodic solutions, the lower bound for the periods is 2π/L. These estimates are achieved for norms that are invariant with respect to permutation of the indices.
About the authors
A. A. Zevin
ITST NAS of Ukraine
Author for correspondence.
Email: alexandr.zevin@gmail.com
Ukraine, Dnieper
References
- Yorke J. // Proc. Amer. Math. Soc. 1969. V. 22. P. 509– 512.
- Mawhin J, Walter W. // JMAA. 1994. V. 186. P. 778798.
- Busenberg S., Fisher D., Martelli M. // Amer. Math. Monthly. 1989. V. 96. P. 5-17.
- Busenberg S., Fisher D., Martelli M. // Proc. Amer. Math. Soc. 1986. V. 86. P. 376-378.
- Зевин А. А. // ДАН. 2012. T. 444. № 6. C. 602-604.
- Zevin A. A. // arXiv.14124539 [math.DS]. 2014.
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