一类泛函的临界点的存在性定理

THE EXISTENCE THEOREMS FOR CRITICAL POINTS OF A CLASS OF FUNCTIONALS

基于逼近理论的思想,我们对无穷维实Hilbert空间上一类泛函引入了一种序列指标(或简称S-指标),并对它在泛函的多重临界点问题中的应用作了讨论,从而在理论上为直接处理无穷维Hilbert空间上一类泛函的临界点问题提供了一种新工具。

Based on the notion of approximation, kind of sequence index (or,for simplicity ,S-index)for a class of functional on an infinite dimensional real Hilbert space is defined,and its significance in the critical point theory is investigated. Hence the S-index as a new theoretical tool to deal with the critical point problems for a class of functionals on the infinite dimensional Hilbert space is introduced.