【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。更多还原

【Abstract】 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.更多还原