条件方程

This paper uses contraction mapping approach in order to give sufficient condition for solvability about this kind of matrix equation in given conditions.

文章利用压缩映射思想给出了一类矩阵方程在给定条件下有解的充分条件。

The principle of minimum potential energy was used to derive the governing differential equation and corresponding boundary conditions.

分析了压杆屈曲时的几何变形条件，导出了压杆的曲率、变形能和各项外力势的表达式，用最小势能原理导出压杆失稳的微分方程和边界条件。

In part 3, utilizing the existing Lipschitz results and the property of Yosida approximation of monotone and continuous function, we prove the existence and uniqueness theorem of a general backward stochastic differential equation with monotone and continuous coefficient.

第三部分在系数仅满足单调连续这样一个新条件下，我们综合运用单调连续函数的Yosida逼近的性质以及Lipschitz条件下的已有结果，证明了一般形式的倒向随机微分方程解的存在唯一性。

The Euler-Lagrange equations and corresponding natural boundary condition are derived by the variation of Ohmic energy dissipation under the constraint of magnetic helicity balance.

在磁螺旋平衡的约束条件下，对总的欧姆耗散取变分，得出了环位形下的Euler_Lagrange方程和自然边条件。

In Chapter 4, we consider the qusilinear elliptic systems with the homogeneous Neumann boundary condition, and obtain the existence and multiplicity of positive solutions.

在第四章中，我们讨论带有齐次Neumann边界条件的拟线性椭圆型方程组(方程和第三章的一样，边界条件不同)，研究了正解的存在性和多解性。

The purpose of Chapter 4 is to study the solvability of multi-point boundary value problems at resonance, and establishs some existence theorems under nonlinear growth restriction. Our method is based upon the coincidence degree theory. In Section 1, we consider the same sign case, and in Section 2, discuss the non-same sign case.

第四章研究了具共振条件下二阶非线性微分方程多点边值问题解的存在性，通过使用重合度理论和一些分析技巧，建立了一系列解存在的充分条件，其中在第一节考虑了同号情形，在第二节考虑了异号情形。

Character of solution of stochastic differential equation in dual of nuclear space was studied.

研究核空间的对偶空间的随机微分方程解的性质，得到微分方程组解 L 2收敛的条件，及在一定条件下解过程导出的测度{ Pn}为胎

When these coefficients are quadratic functions of the porosity, specific constituent orthogonal weighting coefficients are derived from these orthogonal conditions along with a discussion about how to extend the applicable range of the constituent orthogonal weighting coefficients in the orthogonal coordinates. Based on the combination of the theory of critical porosity and the constituent model, it presents a specific example of the constituent model that includes two transforming points. The reasonability of above-mentioned theories is shown by comparison of theoretical calculations and measured data on effective elastic moduli of clean sandstone or sandstone analogs saturated with pure water.

再次，结合弹性模量组分关系方程与正交基函数理论，推导组分加权系数的正交条件；基于正交条件，提出组分加权系数为孔隙度二次多项式时正交组分加权系数的构造方法以及正交组分加权系数适用范围的拓展方法；结合临界孔隙度理论，提出一个基于两个状态分界点的组分模型实例；比较组分模型的计算结果与前人关于砂岩弹性模量的实验结果，证明了组分孔隙介质模型理论的合理性。

New sufficient conditions for allsolutions to be oscillatory are obtained under some very weak conditions.

在较弱的条件下，获得了方程的所有解振动的新的充分条件。

In thrid part we claim that the estimate of the above and of the first initial-boundary value problem for parabolic type equations are still holds under the sec-ond nature structure conditions.

第三节我们说明：第二类自然结构条件下结果也成立，同第一类无多大区别，因而，我们的结果也对第二类自然结构条件下的完全非线性抛物型方程相应的定解问题成立。

For a big chunk of credit-card losses; the number of filings (and thus charge-off rates) would be rising again, whether

年美国个人破产法的一个改动使得破产登记急速下降，而后引起了信用卡大规模的亏损。

Eph. 4:23 And that you be renewed in the spirit of your mind

弗四23 而在你们心思的灵里得以更新