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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Better bounds for periodic solutions of differential equations in Banach spaces


Authors: Stavros N. Busenberg, David C. Fisher and Mario Martelli
Journal: Proc. Amer. Math. Soc. 98 (1986), 376-378
MSC: Primary 34G20; Secondary 34C25
MathSciNet review: 854051
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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.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1986-0854051-6
PII: S 0002-9939(1986)0854051-6
Keywords: Periodic solutions, Lipschitz constant, Wirtmger's inequality, Banach space, Hilbert space, autonomous differential equations
Article copyright: © Copyright 1986 American Mathematical Society