四川大学学报（自然科学版）2025，Vol.62Issue(2)：325-327,3.DOI:10.19907/j.0490-6756.240203
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
摘要
Abstract
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,Lλ(f)≜{x∈X:f(x)≤λ},λ0≜sup{λ∈R:Lλ(f)is bounded},if f∈ C1-0(X,R)is bounded from below and satisfies the(CPS)λ0 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Key words
Ekeland's variational principle/Locally Lipschitz functional/CPS condition/Coercive condition (2020 MSC 49J40,49J45)分类
数学引用本文复制引用
张馨予,张世清..局部Lipschitz泛函的CPS型条件与强制性条件之间的关系[J].四川大学学报（自然科学版）,2025,62(2):325-327,3.基金项目
国家自然科学基金(12071316) （12071316）
