積性線性泛函 的英文怎麼說

中文拼音 [jīxìngxiànxìngfànhán]
積性線性泛函 英文
multiplicative linear functional
  • 積 : Ⅰ動詞（積累） amass; store up; accumulate Ⅱ形容詞（長時間積累下來的） long standing; long pending...
  • 性 : Ⅰ名詞1 （性格） nature; character; disposition 2 （性能; 性質） property; quality 3 （性別） sex ...
  • 線 : 名詞1 （用絲、棉、金屬等製成的細長的東西） thread; string; wire 2 [數學] （一個點任意移動所構成的...
  • 泛 : Ⅰ動詞1 [書面語] （漂浮） float; drift 2 （透出; 冒出） be suffused with 3 （淹沒） inundate; floo...
  • 函 : 名詞1. [書面語] （匣; 封套） case; envelope 2. （信件） letter 3. （姓氏） a surname
  • 線性 : [數學] [物理學] linear; linearity線性代數 linear algebra; 線性方程 linear equation; 線性規劃 line...
  1. 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。
  2. Professor guo dajun has summarized in his work [ 7 ]. such several important tasks and theirs application of nonlinear functional analysis as typical nonlinear operators, hammerstein integral operations, ordinarily and partially differential equations. the cone theory, the positive solutions of nonlinear operator equations, the number and the branch of solutions, and so on. reference [ 1 ] includes all levels of results of the domain such as nonlinear functional analysis

    郭大鈞先生在專著[ 7 ]中對非線性泛函分析的幾個重要課題及其應用，諸如典型的非線性運算元、 hammerstein積分方程、常、偏微分方程、遷移方程、錐理論及非線性運算元方程的正解、非線性運算元拓撲度和不動點定理以及固有值、解的個數與分支，都做了系統的概括和總結
  3. Nonlinear functional analysis is a subject. old but fashionable. its abundant theories and advanced methods are providing powerful and fruitful tools in solving ever increasing nonlinear problems in the fields of science and technology. though the theories of integral and differential equations in banach spaces, as new branches of nonlinear functional analysis. have developed for no more than thirty years, they are finding extensive applications in such domains as the critical point theory, the theory of partial differential equa - tions, eigenvalue problems. and so on, are attracting much more attentions from both pure and applied mathematicians

    非線性泛函分析是一門既悠久又現代的學科，它的豐富理論和先進方法為解決當今科技領域層出不窮的非線性問題提供了卓有成效的工具，作為自非線性泛函分析中衍生發展起來的新的分支， banach空間微分方程和積分方程理論雖經歷了不足三十年的發展過程，然而它已被廣泛應用於諸如臨界點理論，偏微分方程理論，特徵值問題等許多領域，其重要性日益凸現出來
  4. The stability perturbation bounds of a single - input - single - output system with both parametric and dynamic uncertainties is studied. the parametric uncertainties of the systems are described by interval perturbation mode, and the dynamic uncertainties are characterized by an integral quadratic constraint. based on the concepts of the minkowski functional, the problem of stability perturbation bounds is discussed, and for different uncertainty structures of the systems, the infinite stability checking problem of the mixed uncertain system can be converted to finite vertex - checking results and the edge - checking results

    系統的正向通道為帶有參數不確定性的線性系統，其不確定性為區間攝動模式，反饋通道為由積分二次約束給出的輸入輸出不確定性加以描述。用minkowski泛函給出區間攝動模式下的攝動界的定義，並給出參數空間中混合攝動模式下系統攝動界的估計式。
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