查询词典 existence theorem

Chapter 2 discuss firstly the local existence of solutions for a class of abstract functionalintegro-differential equations with unbounded delay by Schauder's fixed point theorem, then byintroducing an inequality condition and applying the continuity property of solutions it obtainsthe global existence of the solutions.

第二章先利用Schauder不动点定理讨论一类具有无限时滞抽象泛函积分微分方程解的局部存在性，然后引入一不等式条件并利用解的延拓性质获得了解的整体存在性

The existence of triple positive solutions for second order multi-point boundary value problem is investigated by using Avery-Peterson fixed point theorem. Gives the sufficient conditions for the existence of three positive solutions of the problems.

研究一类二阶非线性微分方程的n点边值问题正解的存在性，应用Avery-Peterson不动点定理，给出这类边值问题至少存在3个正解的充分条件。

On the basis of Nagumo′s existence theorem for the singular case, we obtain the existence of solutions of singular equations satisfying nonlinear boundary value conditions and periodic boundary value conditions by means of approximations.

在Nagumo型存在定理的基础上，我们应用逼近的方法给出了奇性方程满足非线性边值条件和周期边值条件的解的存在性。

InSection 2,we give several sufficient conditions for the existence of one solution,multiplesolutions and infinitely many solutions of the Sturm-Liouville bvps via the generalizedpolar coordinates.Then in Section 3,the existence of positive solutions are proved undersuperlinearity,sublinearity and many other conditions by a fixed point theorem in cones.Our results have generalized those in many articles.A detailed discussion of periodic solu-tions of a kind of functional differential equations with high-order Laplacian-like operatorcan be found in Section 4 and this subject has not been studied before.

在第二节，我们定义了一种新的坐标变换-广义极坐标，并利用它讨论了p-Laplacian算子和Laplacian-型算子的Sturm-Liouville边值问题，分别得到了存在一个解、多个解、无穷多个解的多个充分条件；第三节研究p-Laplacian算子的Sturm-Liouville边值问题正解的存在性与多重性，采用的是锥上的不动点定理，全面推广了这一方面已有的结果；对目前研究较少的高维Laplacian-型算子及带有Laplacian-型算子的泛函微分方程的周期解问题，我们在第四节做了一些研究，这也是拓扑方法的一个应用。

Thischapter proposes three concepts,i.e.,kernelled quasidifferential,star-kerneland star-differential,and establishes their operational properties.A sufficiencytheorem and a sufficiency and necessity theorem for a quasi-kernel being a ker-nelled quasidifferential are proven.Both the existence of star-kernel for a qua-sidifferentiable function and the existence of star-differential for a directionallydifferentiable function are established.The relationships between sub-and su-per derivatives and Penot differentials are discussed as well.

这一章我们引入了三个概念，即核拟微分，星核与星微分并建立了它们的运算性质；证明了拟核为核拟微分的一个充分条件定理及一个充分与必要条件定理；建立了拟可微函数星核的存在性及方向可微函数星微分的存在性并讨论了Penot微分与上、下导数的关系。

Therefore, this research emphasizes on the learners with personality traits and learning style, and adds knowledge creation factor to see how the learners' responses toward the external stimulators under the E-learning environments. Then this research analyzes the learners' differences on the basic existence and points out that what kind of teaching methods suits the learners best. This research has three results as following: 1.The personality traits and the learning style have the remarkable corresponding relational existence. Openness corresponds to assimilator; Conscientiousness corresponds to converger; Extraversion corresponds to accommodator; Neuroticism corresponds to diverger; Agreeableness has no remarkable correspondence relational existence.

故本研究以人格特质、学习风格等学习者个体本身对於外在环境刺激所反应出的行为，加入知识创造行为，在数位学习的学习环境下进行成效的探讨，分析学习者在根本上所存在的差异，并指出以何种方式进行教学较适合学习者本身，研究结果发现：一、人格特质与学习风格有显著对应的关系存在，聪颖开放人格对应同化型；严谨自律人格对应聚合型；外向人格对应调适型；神经人格对应於分散型；和善人格无显著对应的关系存在。

Huang and Lin proposed the weak solution concept for Backward Stochastic Differential Equation This paper based on the predecessor's work , gives the weak solution concept for Backward Stochastic Differential Equation with continuous martingale,uses the Girsanov transformation, obtains its weak solution of the existence of a necessary and sufficient conditions, and on this basis obtains its weak solution of the existence of sufficient conditions,these sufficient conditions weakened the drifting coefficient which requested in the existence uniqueness of strong solution to satisfy the Lipschitz condition the request.

本文在前人研究的基础上，给出由连续鞅驱动的倒向随机微分方程弱解的概念，利用Girsanov变换，得到其弱解存在的存在的一个充分必要条件，并在此基础上得到了其弱解存在的一些充分条件，这些充分条件减弱了在强解的存在唯一性中要求的漂移系数满足Lipschitz条件的要求。

But the existence in question is no longer the juridical existence of sovereignty; at stake is the biological existence of a population.

但是生存的考虑不再是君主的司法存在；考虑的是人口的生物存在。

The author strictly distinguishes existor from existence, reveals their symmetrical and complemental features and expounds the symmetrical and complemental relation between subjective existence and objective existence.

作者严格区分了在者与存在，揭示出其对称互补的特征，并进而论述了主客体存在的对称互补及其各自的对称互补关系。

This article is divided into four chapters: Chapter I of the existence of Marxist theory on the basis of science and the clarity; chapter of history throughout the domain of the existence of "person" and "Nature" and its relations; Chapter HI of Marx\'s "a science" thinking; conclusion in Chapter IV of the existence of Marxist theory on the scientific understanding of the minds of historical materialism.

本文共分为四章：第一章马克思关于科学的存在论基础的澄明；第二章在历史的存在论境域中的"人"与"自然"及其关系；第三章马克思的"一门科学"思想；第四章结语在马克思关于科学的存在论思想中领会历史唯物主义。

A carrier gas such as nitrogen is directed through line 20 and valve 22 to connect with line 26 and mix with the gas sample.

如氮气之类的载体通过管线20和阀22引入，与管线26相通，与气体样品混合。

But for the most part, knaves and parasites had the command of his fortune

然而支配他的家产的大多是恶棍和寄生虫。