ekeland meaning in English
埃克兰
Examples
- Drop theorem and phelps ' lemma and ekeland ' principle in topological linear spaces
不动点定理及其应用 - In chapter 4 , we give a general result of ekeland ' s variational principle in uniform space
第四章给出了ekeland变分原理在一致空间中的推广。 - Firstly , we validate the functional j ( u ) satisfys the given conditions meets the conditions in the mountain pass lemma without ( ps ) condition , then we use the mountain pass lemma and the famous ekeland theory to prove the existence of two positive solutions
我们首先验证满足假设条件(见正文)的泛函j ( )满足没有( ps )条件的翻山引理中的条件，然后运用没有( ps )条件的山路引理及著名的ekeland变分原理证明两个正解的存在性。 - Chapter 4 is a focal point of the paper . and the generalization of ekeland ' s principle not only broadens its applications - - just as we use it to solve the difficulty of control theory in this paper , but also makes a develop sense in mathematical theory
该章是本文的重点内容之一，其中对ekeland原理的推广不仅使它的应用范围得到了拓广(本文在控制理论方面的应用正是这种拓广的一个实例) ，而且在数学基础理论方面也有一定的发展意义。 - 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。