局部Lipschitz泛函的CPS型条件与强制性条件之间的关系  

On the relationship between coercivity conditions and CPS type conditions of local Lipschitz functional

作　　者：张馨予 张世清[2] ZHANG Xin-Yu;ZHANG Shi-Qing(Hong Kong Baptist University-Beijing Normal University United International College,Zhuhai 519087,China;School of Mathematics,Sichuan University,Chengdu 610064,China)

机构地区：[1]香港浸会大学-北师大联合国际学院,珠海519087 [2]四川大学数学学院,成都610064

出　　处：《四川大学学报(自然科学版)》2025年第2期325-327,共3页Journal of Sichuan University(Natural Science Edition)

基　　金：国家自然科学基金(12071316)。

摘　　要：本文基于Ekeland变分原理及非光滑局部Lipschitz泛函的Clarke广义梯度理论研究了经典强制性条件与张恭庆推广的PS型条件之间的关系.特别地,本文证明:若X是Banach空间且令L_(λ)(f)■{x∈X:f(x)≤λ},λ_(0)■sup{λ∈R:L_(λ)(f)有界},f∈C^(1-0)(X,R)有下界且满足(CPS)_(λ_(0))条件,则f是强制的.In this paper,using Ekeland’s variational principle and Clarke’s generalized gradient theory for non-smooth local Lipschitz functional,we study the relationship between classical coercive condition and Palais-Smale type condition generalized by Gong-Qing ZHANG.Specially,we prove the following result:Let X be a Banach space,L_(λ)(f)■{x∈X:f(x)≤λ},λ_(0)■sup{λ∈R:L_(λ)(f)is bounded},if f∈C^(1-0)(X,R)is bounded from below and satisfies the(CPS)_(λ_(0))condition,then f is coercive.

关 键 词：EKELAND变分原理 局部Lipschitz泛函 CPS条件 强制性条件 

分 类 号：O177.2[理学—数学]