On Ekeland's Variational Principle and a Minimax Theorem
On Ekeland's Variational Principle and a Minimax Theorem
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论埃克兰变分原理和极小极大定理
DOI：
10.1006/jmaa.1996.5168
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发表时间：
1997
影响因子：
1.3
通讯作者：
Cheng
中科院分区：
文献类型：
--
作者：
Cheng
Ekeland的变分原理指出，如果一个Gateaux可微矩阵。函数f有一个有限的下界，尽管它不需要达到它，那么对每个e）0，存在某个点x使得fxFe。本文证明了存在某个点z使得fzFer 1 qeee5 5. W . W . h z，其中h：0，q` a 0，q`是连续非减函数<q`不减函数..这样H 1r 1 q h r dr s q`。作为应用，在弱紧性条件下证明了一个极大极小0定理.
Ekeland’s variational principle states that if a Gateaux differentiable Ž . function f has a finite lower bound although it need not attain it , then 5 Ž .5 for every e ) 0, there exists some point x such that f x F e . This e e 5 Ž .5 Ž paper shows that there exists some point z such that f z F er 1 q e e Ž5 5.. w . w . h z , where h : 0, q` a 0, q` is a continuous nondecreasing func« q`Ž Ž Ž ... tion such that H 1r 1 q h r dr s q`. As an application, a minimax 0 theorem is proved under a weak ‘‘compactness condition.’’