saddle point theorem meaning in English
鞍点定理
Examples
- Lagrange duality and saddle points theorem for multiobjective semidefinite programming
对偶与鞍点定理 - In chapter three , some new glkkm type theorems are proved . these theorems are then applied to obtain some matching theorems , fixed point theorems , a minimax inequality and a saddle point theorem
在第三章中，我们证明了一些广义l ? kkm型定理，然后运用它们得到了一些匹配定理，不动点定理，一个极大极小不等式以及鞍点定理 - In chapter one , r - kkm mappings is discussed . the more general generalized l - r - kkm theorems are established in l - convex space . as applications , a minimax inequalities and a saddle point theorem are obtained in noncompact l - convex spaces
章中，研究了r - kkm映像，在l -凸空间中得到了更为一般的广义l - r - kkm型定理，给出了对极大极小不等式和鞍点存在问题的应用。 - The paper is concerned with periodic solutions to nonautonomous second order hamilton systems where , m : [ 0 , t ] - s ( rn , rn ) is a continuous mapping in the space s ( rn , rn ) of symmetric real ( n x n ) - matrices , such that for some u > 0 and all ( t , z ) [ 0 , t ] x rn , ( m ( t ) x , x ) > u | x | 2 . a s ( rn , rn ) , f : [ 0 , t ] x rn r is continuous and f : [ 0 , t ] xr r exists , is continuous and we study the existence of periodic solutions of the systems by using ekeland variational principle and the saddle points theorem . we suppose that the nonlinearity vf and potential f belongs to a class of unbounded functional . our work improves the existed results . we obtained the results of multiplicity of periodic solutions of the systems by using lusternik - schnirelman category theory and the generalized saddle points theorem , and the functional does not need the condition of constant definite . at last , we obtained the existence of infinity many distinct periodic solutions of the corresponding non - perturbation systems by using the symmetric mountain pass theorem
( ? ， ? )为r ~ n中内积， | ? |为对应范数。 f [ 0 ， t ] r ~ n r连续， ? f ( t ， x )存在且连续， h l ~ 1 ( 0 ， t ； r ~ n ) 。利用ekeland变分原理和鞍点定理讨论了该系统周期解的存在性，把非线性项和位势函数放宽到一类无界函数，推广了这方面工作的一些已有结果；利用广义鞍点定理和lusternik - schnirelman畴数理论得到了该系统的多重周期解，取掉了泛函的常定要求；最后利用对称山路定理得到没有扰动时系统的无穷多周期解。 - At first , we introduce a class of generalized s - r - kkm type mapping in g - convex space , and establish generalized s - r - kkm type nonempty intersection theorem under the noncompact setting of g - convex space . as for application , some new minimax inequalities , saddle point theorem and existence theorem of maximal elements are proved in g - convex spaces ; second , by using the generalized r - kkm mapping and generalized r - kkm theorems in [ 13 ] , some new existence theorem of maximal elements , existence theorem of equilibrium point for the abstract generalized vector equilibrium problem and existence theorem of solutions for equilibrium problem with lower and upper bounds are obtained in topological spaces
首先，我们在g -凸空间内引入了广义s - r - kkm型映像，并在非紧设置下建立了一类新的广义s - r - kkm型非空交定理，作为应用，证明了g -凸空间内一些新的极大极小不等式、鞍点定理和极大元存在定理；其次，利用文[ 13 ]中引入的广义r - kkm映像和广义r - kkm定理，在拓扑空间上得到了一些新的极大元存在定理、抽象广义矢量平衡问题平衡点的存在定理和有上下界的平衡问题解的存在性定理。