摘要
本文证明如下定理:设J,T_1,…,T_m都是定义在赋范空间X上的可微实泛函,而1_1…1_m是实数,如在条件T_j(x)=1_j(j=1,…,m)限制下,泛函J在x_0∈X处达到极值,则必存在实常数λ_1,…,λ_m,使泛函G=J+λ_1T_1+…+λ_mT_m在x。处的变分为零。
This paper proves the following theorem: let J, T_1, ..., T_m be differentiable real functionals defining on the normed space X, and l_1,…, l_m be real numbers. If under the conditions T_j(x)=l_j; j=1,…, m functional J takes extreme value at x_0∈X, then there exist real constants λ_1, …, λ_m, which make the variation of functional G=J+λ_1T_1+…+λ_mT_m at x_0 equal to zero.
关键词
赋范空间
泛函
拉格朗日乘数
变分
normed space
functional
variation
extreme value Lagrange's method of multipliers
