[計][數] 存在性定理
As its application, we give a new proof of the existence theorem of prime models.
作為其應用，我們給出了素模型存在定理的另一種證明。
In the paper, Existence theorem for generalized variational inequalities is established in locally FC-spaces space and its applications are presented.
文章提供關于局部FC-空間上的廣義變分不等式的存在性定理，并給出它的一些應用。
Using the method of boundary layer correction and the differential inequality theory, we prove the existence theorem of solutions and construct the uniformly valid asymptotic expansions of .
我們利用邊界層校正法以及微分不等式理論證明了解的存在定理，并構造出其解的一緻有效漸近展開式。
The existence theorem shows that the equation has at least one solution provided the nonlinear term satisfies a linear growth condition.
這個存在定理說明隻要非線性項滿足某種線性增長條件該方程至少有一個解。
An existence theorem of continuous signal transfer operator is given.
證明了連續信號傳輸算子的存在定理。
An existence theorem of periodic solutions was obtained for non-autonomous second order systems with sub-additive potential by using the least action principle.
通過使用最小作用原理，對于具有次可加位勢的非自治二階系統，獲得了一個周期解的存在性定理。
By using a universal method a new existence theorem of solution for a generalized equilibrium problem in topological vector space is obtained.
通過一種具有普遍意義的方法，線上性拓撲空間中獲得一個新的廣義平衡問題解的存在性定理。
Using the principal curvature formula, we prove an existence theorem of Weingarten hypersurface.
并利用主曲率計算公式證明了W-超曲面的一個存在性定理。
In this paper, the author discusses the existence of solutions to initial boundary value problem of nonlinear parabolic equations and obtains the existence theorem.
讨論了一類非線性抛物型方程的初邊值問題解的存在性，并得出了解的存在性定理。
In the present paper, the non-autonomous second order systems are stu***d by the minimax methods in critical point theory and a existence theorem of periodic solutions is obtained.
通過使用臨界點理論中的極大極小方法研究了以下非自治二階哈密頓系統并獲得了一個周期解的存在性定理。
An existence theorem of twin positive solutions is established for a nonlinear fourth-order two-point boundary value problem.
對于非線性四階兩點邊值問題建立了一個孿生正解的存在定理。
In this paper, to 1-set contraction random operator equation, the author explained the conception of couple solution, obtained existence theorem of couple solution.
提出了1-集壓縮型隨機算子方程耦合解的概念，并研究了這類隨機算子方程耦合解的存在性。
A new existence theorem on cyclic difference sets is introduced in this note.
本文介紹了一個循環差集的存在性定理。
Under a suitable condition, this paper gives an existence theorem for harmonic maps from surfaces to certain Riemannian manifolds in a large scale.
在一定條件下，給出了一個從曲面出發的大範圍調和映照的存在性定理。
For the non-homogeneous multi-dimensional scalar conservation laws, there is no existence theorem of global weak solution.
關于高維單守恒律方程的研究，對于非齊次的情形，至今還沒有得到全局弱解的存在性定理。
We introduce concepts of diagonal quasi-convexity and quasi-concavity in hyperconvex metric spaces, and prove an existence theorem for equilibrium problems.
引進超凸度量空間的對角拟凸和拟凹概念，并證明一類均衡問題解的存在性。
Existence theorem for optimal portfolio is provided.
證明了最優組合投資的存在性；
Firstly, based on the staged unstructured model of Nosiheptide fermentation process, secondary variables were selected according to the implicit function existence theorem.
首先以分階段的諾西肽發酵過程非結構模型為基礎，根據隱函數存在定理進行輔助變量的合理選擇；
Author study essential components problems of the equilibrium point set of generalized games and give an existence theorem.
研究廣義對策平衡點集的本質連通區問題，證明了存在性。
The proof of existence theorem is given.
證明了存在定理。
By using weak noncompact types conditions, we obtain an existence theorem of generalized weak solutions to (cp), improving the results of weak solutions in , .
讨論模的同态的群逆存在的條件，得到正則自同态的群逆通過弱廣義逆表示的顯式，并給出一些應用和例子。
In this paper, we consider the existence of multiple positive solutions of discrete boundary value problem. The theory of fixed point index is used here to derive the existence theorem.
本文利用不動點指數理論得到離散邊值問題多重正解的存在性。
This paper discusses average approximation and proposes four theorems which are the supplement for existence theorem, characteristic theorem and solitariness theorem.
本文讨論了平均逼近，給出了四個定理，是對存在定理、特征定理，唯一性定理的補充。
A new existence theorem is obtained by applying the degree theory on cone.
利用錐上的度數理論獲得了一個新的存在定理。
In this paper the author establish a new fixed point theorem of multivalued mapping, and then prove an existence theorem of equilibrium for abstract economies as its application.
在局部凸空間中對集值映射建立一個新的不動點定理。作為應用，給出了一個抽象經濟的平衡存在性定理。
By using a known fixed point theorem, an existence theorem of solutions of generalized variational inequality is proved in noncompact H space.
利用已知的不動點定理，在非緊H空間内得到抽象廣義變分不等式解的存在性定理；
The degree theory is applied to obtain an existence theorem for the fourth-order two-point boundary value problem with asymptotic nonlinearity.
利用拓撲度理論獲得了一個漸近非線性四階兩點邊值問題的存在定理。
Given the definition of P2-Asymptote and established P2-asymptote existence theorem.
給出了P2-漸近線的定義，得到了P2?漸近線存在定理。
As am example of application, the existence theorem of random solution for random operator equations is given.
同時給出了隨機算子方程組公共隨機解的一個存在性定理。
存在性定理（Existence Theorem）是數學中一類證明特定對象或解存在的核心定理，其核心價值在于通過嚴謹的邏輯推導确認數學實體的存在性，而非構造具體實例。這類定理在現代數學分析、微分方程和拓撲學等領域具有基礎性作用。
經典案例解析：
壓縮映射原理（巴拿赫不動點定理）：在完備度量空間中，滿足壓縮條件的映射必存在唯一不動點。該定理為微分方程解的存在唯一性提供了基礎框架，被廣泛應用于工程計算和經濟學模型穩定性分析。參考來源：Kreyszig, E. (1978). Introductory Functional Analysis with Applications.
皮卡-林德洛夫定理：證明滿足利普希茨條件的常微分方程初值問題在局部範圍内存在唯一解。這為動力系統建模提供了嚴格的理論保障，在航天器軌道計算和生物種群模型預測中發揮關鍵作用。參考來源：Teschl, G. (2012). Ordinary Differential Equations and Dynamical Systems.
學科應用特征：存在性定理與構造性方法形成方法論互補，在偏微分方程研究中，先确立解的存在性往往成為構建具體解的前提條件。這種方法論特色體現了現代數學對邏輯嚴謹性的追求，在理論物理的量子場論建構過程中展現重要價值。參考來源：Wolfram MathWorld, Existence Theorem.
存在性定理（Existence Theorem）是數學中的一個重要概念，指通過邏輯推理證明某種數學對象（如方程的解、特定結構或性質）在一定條件下必然存在，但無需具體構造出該對象的定理。以下是詳細解釋：
存在性定理的核心在于“存在性”的證明，而非具體如何找到或描述該對象。例如：
存在性定理因“非構造性”曾被質疑（如直覺主義學派），但其在推動數學發展中的作用不可替代。現代數學中，兩者常結合使用：先證存在性，再研究構造方法。
若需具體領域（如分析、拓撲）的存在性定理實例，可提供進一步說明。
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