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Shorter Notes: Better Bounds for Periodic Solutions of Differential Equations in Banach Spaces

Stavros N. Busenberg, David C. Fisher and Mario Martelli
Proceedings of the American Mathematical Society
Vol. 98, No. 2 (Oct., 1986), pp. 376-378
DOI: 10.2307/2045716
Stable URL: http://www.jstor.org/stable/2045716
Page Count: 3
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Shorter Notes: Better Bounds for Periodic Solutions of Differential Equations in Banach Spaces
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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 ≥ 6/L. An example is given with P = 2π/L, so the bound is nearly strict. We also give a short proof that P ≥ 2π/L in a Hilbert space.

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