查询词典 Liouville theorem

This paper is in the comparison theorem of Sturm-Liouville problem, based on the type of separation is given.

该文讨论了一类分离边界条件下的Sturm-Liouville特征值问题，就不同的势函数q，分别在右定和左定情形下建立了特征值的比较定理。

harmonic function ; Liouville theorem ; Dirichlet integral ; relative compact domain

并得到 次调和函数的Liouville定理和具有有限的 Dirichlet积分的次调和函数的性质。

As for the existence of positive solutions, the cone theory and the fixed point index of condensing mapping are employed, and the results of the existence of positive solutions are obtained in the case of superlinear and sublinear. The conclusions extend and improve the existence theorem which Lou Ben-dong extablished in 1996 about the question of Sturm-Liouville of Banach spaces.

三、对于正解存在性问题，我们应用凝聚映射的不动点指数理论，分别在超线性与次线性情形下进行讨论，获得了一些正解存在的结果，主要结果推广和改进了1996年Lou Ben-dong对Banach空间Sturm-Liouville问题所建立的存在性定理。

Under Sturm-Liouville conditions, the existence of at least three positive solutions is proved by using Leggett-Williams fixed point theorem.

利用Leggett-Williams不动点定理，研究了在Sturm-Liouville边界条件下的一类二阶常微分方程组多个正解的存在性，得到了至少三个正解存在的充分条件。

This paper weakened the Liouville s theorem conditions,and gives the Liouville theorem of a promotion.

弱化了刘维尔定理的条件，给出了刘维尔定理的一个推广。

By means of classical analytic method and combinatorial computational technique, such as functional equations, Liouville theorem, series rearrangements, this dissertation investigates the product identities on theta functions.

利用经典分析方法及组合计算技巧，例如函数方程，Liouville定理，级数重排等，本文着重研究theta函数中的乘积恒等式。

An integrated Hamiltonian theory was constituted in Classical Mechanics and applied to studying the form of Lagrange equation in theory of electromagnetic, the Schrodinger equation and the Liouville theorem in statistical Physics.

经典力学利用Hamilton系统建立了一套完整的Hamilton理论，用以研究电磁场理论的拉格朗日方程形式，薛定谔波方程，统计物理学中的Liouville定理等。

In this project, we have mainly researched the complex-anlyticity,constancy and stability of pluriharmonic maps to complex grassmannian manifolds;the characterization and isotropicity of pluriharmonic maps with finite uniton number;the regularity, singularty and Liouville theorem of harmonic maps.

本课题着重研究到复Grassmann流形多重调和映照的复分析、常值性及稳定性之间的关系；具有有限uniton数的多重调和映照的特征与迷向性；调和映照的正则性、奇异性及Liouville定理。

Liouville"s Theorem on entire functions is proposed as a proving method for theta function identities. Several identities are exemplified, such as the quintuple and septuple product identities; four symmetric difference identities related to the Ramanujan"s congruence modulo 11 on the partition function; as well as two theta function identities on the Rogers-Ramanujan functions G and H.

作者提出利用Liouville定理作为证明theta函数恒等式的基本方法，并以Watson五重积，Hirschhorn七重积恒等式，四个与分拆函数中Ramanujan的模11同余有关的对称差恒等式，以及两个与Rogers-Ramanujan函数G，H有关的theta函数恒等式为范例，论证这种方法的有效性。

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。

What are your goals and strategies for growth?

你的成长目标和策略是什么？

And unto the angel of the church in Sardis write; These things saith he that hath the seven irits of God, and the seven star I know thy works, that thou hast a name that thou livest, and art dead.

3：1 你要写信给撒狄教会的使者，说，那有神的七灵和七星的，说，我知道你的行为，按名你是活的，其实是死的。