ekeland 中文意思是什麼
ekeland
解釋
埃克蘭-
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
（ ? ， ? ）為r ~ n中內積， | ? |為對應范數。 f [ 0 ， t ] r ~ n r連續， ? f （ t ， x ）存在且連續， h l ~ 1 （ 0 ， t ； r ~ n ） 。利用ekeland變分原理和鞍點定理討論了該系統周期解的存在性，把非線性項和位勢函數放寬到一類無界函數，推廣了這方面工作的一些已有結果；利用廣義鞍點定理和lusternik - schnirelman疇數理論得到了該系統的多重周期解，取掉了泛函的常定要求；最後利用對稱山路定理得到沒有擾動時系統的無窮多周期解。 -
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
該章是本文的重點內容之一，其中對ekeland原理的推廣不僅使它的應用范圍得到了拓廣（本文在控制理論方面的應用正是這種拓廣的一個實例） ，而且在數學基礎理論方面也有一定的發展意義。 -
In chapter 4, we give a general result of ekeland ' s variational principle in uniform space
第四章給出了ekeland變分原理在一致空間中的推廣。 -
Replacing the ekeland distance by an uniform topology. endued with the new structure, uad is free of uncompleted of the old structure under unbounded control situation. meanwhile, the generalized ekeland ' s principle can be used to probe into the infinite time interval and unbounded control problems
用一種一致結構代替以往文獻中賦予uad的ekeland度量結構，從而解決了在討論無界控制時uad的原結構所遇到的不完備性問題；同時，我們對ekeland原理的推廣，也使該原理可用來討論無限時間區域、無界控制條件下的最優控制問題。 -
Drop theorem and phelps ' lemma and ekeland ' principle in topological linear spaces
不動點定理及其應用 -
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
我們首先驗證滿足假設條件（見正文）的泛函j （ ）滿足沒有（ ps ）條件的翻山引理中的條件，然後運用沒有（ ps ）條件的山路引理及著名的ekeland變分原理證明兩個正解的存在性。
分享友人