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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
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