一类无界函数的变分原理  

A variational principle for a class of function without lower bounds

作　　者：孙帆[1] 杨国志[1] 

机构地区：[1]河南质量工程职业学院,河南平顶山467000

出　　处：《南阳师范学院学报》2009年第9期25-27,共3页Journal of Nanyang Normal University

摘　　要：研究了定义在Banach空间上在每个有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f可以加上单调函数、连续凸函数、可微凸函数使它转为有界函数,再利用有下界的变分原理,得到无界函数的变分原理.In the paper, we investigate 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, we prove that adding to a monotonic function, or a continuous convex function, or a differentiable convex function can turn f into a lower bounded function. Then using the varia tional principle with lower bound, we get the variational principle of functions without bound.

关 键 词：BANACH空间 下半连续 β-可微 变分问题 

分 类 号：O177.2[理学—数学]