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首页> 外文期刊>Ricerche di Matematica >On the Ekeland–Ghoussoub–Preiss and Stuart criteria for locating Cerami sequences
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On the Ekeland–Ghoussoub–Preiss and Stuart criteria for locating Cerami sequences

机译：关于确定切拉米序列的Ekeland–Ghoussoub–Preiss和Stuart标准

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摘要

A classical result of Ekeland, based on an idea of Ghoussoub and Preiss, asserts that under technical conditions, Cerami sequences for a real valued functional ${Phi}$ on a Banach space X can be found in the vicinity of suitable closed subsets W of X. In this statement, “vicinity” is defined by means of an associated geodesic distance on X. Recently, under virtually the same hypotheses, Stuart discovered a similar property with a much clearer content since it can very simply be expressed in terms of the norm of X and the corresponding standard distance. In this paper, we prove that the Ekeland–Ghoussoub–Preiss and Stuart criteria are in fact equivalent. We also show that this equivalence need not be true when Cerami sequences are replaced by more general, yet admissible sequences, but that the equivalence is preserved, in part or in totality, under simple additional conditions. These results are also applicable to more general linking geometries than considered by Ekeland–Ghoussoub–Preiss or Stuart and to nonsmooth functionals.
机译：基于Ghoussoub和Preiss的思想，Ekeland的经典结果断言，在技术条件下，可以在Banach空间X上合适的闭合子集W的附近找到C的实值序列$ {Phi} $的Cerami序列。 X。在此陈述中，“邻近度”是通过X上的相关测地距离定义的。最近，在几乎相同的假设下，Stuart发现了具有更清晰内容的相似属性，因为可以非常简单地用X来表示。 X的范数和相应的标准距离。在本文中，我们证明Ekeland–Ghoussoub–Preiss和Stuart标准实际上是等效的。我们还表明，当Cerami序列被更通用但可允许的序列代替时，这种等效性并不一定成立，而是在简单的附加条件下部分或全部保留了等效性。这些结果还适用于比Ekeland–Ghoussoub–Preiss或Stuart所考虑的更通用的连接几何，以及非光滑的功能。

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