existence and uniqueness theorem 中文意思是什麼

existence and uniqueness theorem 解釋
存在和唯一定理
  • existence : n. 1. 存在，實在，繼續存在。2. 生存，生活，生活方式。3. 實體，存在物，生物。
  • and : n. 1. 附加條件。2. 〈常 pl. 〉附加細節。
  • uniqueness : （惟一性）選項組。利用該組參數，通過設置其下方的種子數值，可以在相同的參數設置下產生不同的隨機效果，以確保其隨機性。
  • theorem : n. 1. （能證明的）一般原理，公理，定律，法則。2. 【數學】定理。
  1. The global inverse function theorem is applied for the existence and uniqueness of periodical solutions to the semilinear boundary value problems. some results are improved

    摘要本文運用整體反函數理論證明了一類半線性方程邊值問題周期解的存在唯一性，推廣和改進了已有的一些結果。
  2. The equations of the mean value functions and the covariance functions are established for dynamical systems whose inputs are fuzzy stochastic processes. an existence and uniqueness theorem of ito fuzzy stochastic differential equations is proved, some explicit representations of solutions and the equations of statistical characteristics are deduced for linear fuzzy stochastic differential equations, and numerical methods to nonlinear fuzzy stochastic differential equations are proposed, the conditions for stability and observability of fuzzy linear systems are derived. the kalman filter algorithms of linear fuzzy stochastic systems are brought forward

    主要成果包括：提出了模糊隨機變量協方差和反向協方差的概念；研究了二階模糊隨機變量的均方收斂性，並在此基礎上得到了均方模糊隨機分析、平穩模糊隨機過程及其譜分解的若干定理；根據均方模糊隨機分析理論，得到了輸入為模糊隨機過程的線性系統的輸出輸入統計特徵關系方程；證明了ito型模糊隨機微分方程解的存在唯一性，並給出了ito型線性模糊隨機微分方程解的表達式，統計特徵方程以及非線性模糊隨機微分方程的數值解法；得到了模糊線性系統的穩定性和可觀性條件、線性模糊隨機系統統計特徵方程和線性模糊隨機系統的kalman濾波演算法；研究了當觀測值是模糊數據時，線性回歸模型的建立。
  3. An existence and uniqueness theorem of limit cycles for li 233 ; nard system

    極限環的一個存在唯一性定理
  4. We reduce the cauchy problem of equations ( 8 ), ( 9 ) to an equivalent integral equations by the fundamental solution of a second order partial differential equation. then using the contraction mapping principle and the extension theorem of the solution we prove the existence and uniqueness of the global generalized solutions and the existence and uniqness of the global classical solution

    先是通過一個二階偏微分方程的基本解，把imbq型方程組歸） ， p ）的初值問題轉化為等價的積分方程組，然後利用壓縮映射原理、解的延拓定理等證明了歸） ，問的初值問題的整體廣義解和整體古典解的存在唯一性
  5. In chapter two, under non - lipschitz condition, the existence and uniqueness of the solution of the second kind of bsde is researched, based on it, the stability of the solution is proved ; in chapter three, under non - lipschitz condition, the comparison theorem of the solution of the second kind of bsde is proved and using the monotone iterative technique, the existence of minimal and maximal solution is constructively proved ; in chapter four, on the base of above results, we get some results of the second kind of bsde which partly decouple with sde ( fbsde ), which include that the solution of the bsde is continuous in the initial value of sde and the application to optimal control and dynamic programming. at the end of this section, the character of the corresponding utility function has been discussed, e. g monotonicity, concavity and risk aversion ; in chapter 5, for the first land of bsde, using the monotone iterative technique, the existence of minimal and maximal solution is proved and other characters and applications to utility function are studied

    首先，第二章在非lipschitz條件下，研究了第二類方程的解的存在唯一性問題，在此基礎上，又證明了解的穩定性；第三章在非lipschitz條件下，證明了第二類bsde解的比較定理，並在此基礎上，利用單調迭代的方法，構造性證明了最大、最小解的存在性；第四章在以上的一些理論基礎之上，得到了相應的與第二類倒向隨機微分方程耦合的正倒向隨機微分方程系統的一些結果，主要包括倒向隨機微分方程的解關于正向隨機微分方程的初值是具有連續性的，得到了最優控制和動態規劃的一些結果，在這一章的最後還討論了相應的效用函數的性質，如，效用函數的單調性、凹性以及風險規避性等;第五章，針對第一類倒向隨機微分方程，運用單調迭代方法，證明了最大和最小解的存在性，並研究了解的其它性質及在效用函數上的應用。
  6. By constructing the conditions consistent with its solution, and employing the theorem of the immobile point in functional analysis, it is proved that the existence and uniqueness of the local m - estimate with some conditions

    摘要通過構造解存在所滿足的條件及引入泛函分析中的不動點定理證明了穩健的變窗寬局部線性回歸估計在一定條件下解的存在性和唯一性。
  7. 2. by doing precise computation of spectral radius of linear operator of linear equation and by using measure of noncompactness and leray - schauder type fixed point theorem of condensing mapping, the existence and the uniqueness of the solutions are obtained, which extend the results recently achieved in this field

    二、通過線性方程解運算元譜半徑的論證，在緊型條件下利用凝聚映射的leray - schauder不動點定理及冪壓縮映射不動點定理，獲得了解的存在性與唯一性結果，這些結果推廣了近期這方面已有的一些結果。
  8. In this paper, we use the coupled fixed point theorem for mixed monotone condensing operators to obtain an existence, uniqueness and iterative approximation theorem of solutions of initial value problems for second order mixed monotone type of impulsive differential equations

    利用混合單調凝聚運算元的耦合不動點定理，給出了二階混合單調型脈沖微分方程的初值問題的解的存在唯一性及迭代逼近定理
  9. Existence and uniqueness are proved by lax - milgram theorem for a type of degenerate divergence elliptic equation in a type of sobolev spaces with weight, and also the regularity will be studied

    先用lax - milgram定理證明一類退化散度型橢圓型方程在帶權sobolev空間中弱解的存在唯一性，然後證明解的正則性。
  10. Some basic concepts and results are stated. in chapter 2, a kind of quasi - linear iterative equations has been discussed. existence, uniqueness and stability of the continuous solutions of the equation are proved by using fixed point theorem

    在本文的第二章中對一類擬線性迭代方程進行了討論，運用函數空間上的不動點定理給出了方程連續解的存在性，並進一步研究了解的唯一性和穩定性。
  11. A common fixed point theorem for compatible mappings of type ( a ) is proved and a application to the existence and uniqueness of solutions of system of functional equations in dynamic programming is given

    摘要證明了（ a ）型相容映射的一個公共不動點定理，並討論了起源於動態規劃的泛函方程組的解的存在性和唯一性。
  12. Assume that. in this paper, we will discuss the existence, the non - existence and the uniqueness of limit cycle system ( * ). the methods employed are poincare - bendixsion theorem, method of dulac function and zhang zhifen ' s uniqueness theorem. our main results are as follows : theorem 1

    對的情形，我們討論了系統（ * ）極限環的存在性、不存在性和唯一性。主要利用環域定理、 dulac函數法和張芷芬的唯一性定理等手法。
  13. In the third chapter, we derive a new family of deformed halley methods without the evaluation of the second frechet - derivative to approximate the roots of nondifferentiable equations in banach space. we also provided a existence - uniqueness theorem and a new system of recurrence relations

    在第三章中，構造了一族避免二階fre chet導數的修正halley迭代，用其去逼近banach空間中非線性運算元方程的解，同時給出了存在唯一性定理和一種新型的遞歸關系。
  14. This paper mainly discusses the periodic solutions of some integral and differential equations with infinite delay. the studies of the existence and uniqueness of the periodic solutions and the stabilities of these equations have attracted great concern in recent years and many good results have been obtained. this paper has further extended these conclusions on the foundations of them, and obtained some new results with the method of exponential dichotomy, fixed point theorem and liapunov functional respectively

    本文主要討論具有無窮時滯積分微分方程的周期解。對于這類方程周期解的存在唯一性和穩定性的研究近年來已經引起人們極大的關注，也得到了若干很好的結果。本文主要是在這些結果的基礎上將已有結論做了進一步的推廣，分別用指數型二分性，不動點定理， liapunov泛函的方法得到一些新的結論。
  15. In this paper, based on the method of variable replacement, real parameters di > 0 ( i = 1, 2, . ., n ) which can be adjusted, are introduced ingeniously. we establish some new sufficient conditions for the existence, uniqueness and global exponential stability of the equilibrium, periodic solution and almost periodic solution of neural networks with time - varying delays by means of the method of variation of parameters, fixed point theorem and some analysis techniques

    本文巧妙地引入可調實參數d _ i 0 （ i = 1 ， 2 ， … ， n ） ，藉助常數變易法、變量替換、不動點定理和一些分析技巧，對具可變時滯的神經網路的平衡點、周期解、概周期解的存在性和全局指數穩定性建立了一些新的充分條件。
  16. This dissertation focuses on the locally classical solution and the globally classical solution of one dimensional combustion free boundary problem. the existence and uniqueness of classical solution locally in time will be obtained by the use of fixed point theorem

    本文集中於對一個一維燃燒問題的局部古典解和整體古典解進行研究，應用不動點定理得到局部古典解存在唯一性。
  17. This paper study the character and application of the solution of bsde, the main results include : for the second kind of bsde, the existence and uniqueness of the solution under non - lipschitz condition, comparison theorem and stability are established, under weaker condition, the existence of the minimal and maximal solution is proved and the application in stochastic control and utility function is given ; for the first kind of bsde, under weaker condition, the existence of minimal and maximal solution. stability, comparison theorem and application to utility function are proved

    本文研究倒向隨機微分方程解的性質及其應用，主要結果有：針對第二類方程，討論了在非lipschitz條件下倒向隨機微分方程解的存在唯一性，比較定理及穩定性等，在更弱條件下，得到了倒向隨機微分方程的最大解和最小解的存在性，在此基礎之上，給出了在隨機控制及效用函數方面的應用；針對第一類方程，同樣在較弱條件下，證明了方程最大、最小解的存在性、穩定性、比較定理及其在效用函數的應用。
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