Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 34G20, 34C25

Retrieve articles in all journals with MSC: 34G20, 34C25

Additional Information

Keywords: Periodic solutions, Lipschitz constant, Wirtmger's inequality, Banach space, Hilbert space, autonomous differential equations
Article copyright: © Copyright 1986 American Mathematical Society

American Mathematical Society