Better bounds for periodic solutions of differential equations in Banach spaces
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- by Stavros N. Busenberg, David C. Fisher and Mario Martelli PDF
- Proc. Amer. Math. Soc. 98 (1986), 376-378 Request permission
Abstract:
Let $f$ be Lipschitz with constant $L$ in a Banach space and let $x(t)$ be a $P$-periodic solution of $x’(t) = f(x(t))$. We show that $P \geqslant 6/L$. An example is given with $P = 2\pi /L$, so the bound is nearly strict. We also give a short proof that $P \geqslant 2\pi /L$ in a Hilbert space.References
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W. Blaschke, Kries und Kugel, Chelsea, New York, 1916.
- S. Busenberg and M. Martelli, Bounds for the period of periodic orbits of dynamical systems, J. Differential Equations 67 (1987), no. 3, 359–371. MR 884275, DOI 10.1016/0022-0396(87)90132-X
- A. Lasota and James A. Yorke, Bounds for periodic solutions of differential equations in Banach spaces, J. Differential Equations 10 (1971), 83–91. MR 279411, DOI 10.1016/0022-0396(71)90097-0
- James A. Yorke, Periods of periodic solutions and the Lipschitz constant, Proc. Amer. Math. Soc. 22 (1969), 509–512. MR 245916, DOI 10.1090/S0002-9939-1969-0245916-7
Additional Information
- © Copyright 1986 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 98 (1986), 376-378
- MSC: Primary 34G20; Secondary 34C25
- DOI: https://doi.org/10.1090/S0002-9939-1986-0854051-6
- MathSciNet review: 854051