English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Let x(t) be a non-constant T-periodic solution to the ordinary differentialequation x'= f(x) in a Banach space X where f is assumed to be Lipschitzcontinuous with constant L. Then there exists a constant c such that T L >= c,with c only depending on X. It is known that c >= 6 in any Banach space andthat c = 2{\pi} in any Hilbert space, but whereas the bound of c = 2 pi issharp in any Hilbert space, there exists only one known example of a Banachspace such that c = 6 is optimal. In this paper, we show that the inequality isin fact strict in any strictly convex Banach space. Moreover, we improve thelower bound for l^p(R^n) and L^p(M, {\mu}) for a range of p close to p = 2 byusing a form of Wirtinger's inequality for functions in W^{1,p}([0, T ], L^p(M,{\mu})).

Minimal Periods for Ordinary Differential Equations in Strictly Convex Banach Spaces and Explicit Bounds for some l^p-Spaces