Banach空间中无下界函数的变分问题  

Variational Problem of Function Without Lower Bounds in Banach Space

作　　者：孙帆[1] 杨国志[1] 李保安[2] 

机构地区：[1]河南质量工程职业学院,河南平顶山467000 [2]河南科技大学理学院,河南洛阳471003

出　　处：《河南科技大学学报（自然科学版）》2009年第5期86-88,共3页Journal of Henan University of Science And Technology:Natural Science

基　　金：国家自然科学基金项目(50378030);河南省教育厅自然科学研究计划项目(2007560011)

摘　　要：主要研究了定义在Banach空间上在每个有子界集上有下界但在整个空间上可能无界的广义实值下半连续函数f的变分问题。首先证明了如果f和一个大于0的连续函数Φ的比值在x→+∞时大于一个常数α,则f-αΦ必有下界,然后再利用有下界的变分原理,即得到无界函数的变分原理。This paper expounds the variational problem of extended real valued lower semi-continuous functions defined on real Banach spaces that are lower bounded on every bounded set,but may be not lower bounded on the whole space.First,it is proved if the ratio of f to Φ(Φ > 0) is larger than a constant α under the conditionx→+∞,f-αΦ has a lower bound.Then applying the variational principle with lower bound,the variational principle of functions without bound will be got.

关 键 词：BANACH空间 下半连续 β-可微 变分问题 

分 类 号：O177.91[理学—数学]