然后根据这个估计式，将问题化成求解一个条件变分问题。
Using this estimate, it may be simplified to solve a problem of the conditional variation.
同时从能量最小原理出发，用变分的方法推导出几种端值条件，说明它们的力学背景。
Some end value condition derived by variational method in accordance with the least energy loss principle and their mechanical background are also dealt with.
文中引入了一类广义不变凸函数，对一类变分问题给出了最优解的充分性条件以及对偶理论。
The generalized invex functions are introduced and the optimality theorems and duality theory are established for a class of variational problems.
建立了管道泄漏引起的水力瞬变泄漏数学模型和边界条件，构造了差分方程。
Mathematics model and boundary conditions are proposed for hydraulic transient which is resulted from pipeline leaking while the difference equation is constructed.
然后利用拉格朗日乘子法，吸收第一类边界条件，从而得出其广义变分原理；
Then its generalized variational principle is established on the basis of Lagrange multiplier method by absorbing the first kind of boundary condition.
使用变分方法，推导了这类反应器边界温度控制的必要条件。
Using variational calculus, necessary conditions for boundary temperature control of the reactors have been derived.
利用变分原理得到平衡微分方程组和相应的边界条件。
By variational principle we obtain a system of differential equations and corresponding boundary conditions.
在比（AR）条件更弱的一类超线性条件之下，利用变分方法讨论了一类超线性四阶椭圆方程的无穷多解的存在性。
By means of the variational approach, in a condition weaker than(AR) the existence of infinitely many solutions of fourth-order elliptic equation is discussed.
弹性力学变分原理的先决条件、补充条件和反映的规律一起正是弹性力学全部基本方程。
The preconditions, additional conditions and reflection laws of variational principle are the complete elementary equations in elasticity.
提出了一个包括界面条件及间断面条件在内的混合边值问题的广义变分原理，建立了极限载荷乘子的变分解析公式。
A generalized variational principle involving conditions of the rigid-plastic interface and the discontinuous surface of a velocity field has been put forward for the mixed-boundary value problem.
另一种处理方法是只对弥散项实施积分变换，应用边界条件，得出变分方程。
The other method is to perform the integration by parts only to dispersion term, then introduce the boundary conditions, and finally obtain the variation equation.
应用拉氏乘子法推导有先决条件的广义变分原理。
The derivation of generalized variational principles with preconditions by the use of the Lagrange multiplier method.
利用能量泛函变分的方法导出了发生弹性失稳的非经典边界条件，得到了失稳的判据方程。
The non-classic boundary condition of the elastic instability has been educed by the energy functional variation analysis. So a criterion equation of the elastic instability can be got.
在具有变分结构条件下推广了锐角原理。
The acute Angle theorem is extended under the condition of the variational structure.
明确了虚位移原理的变分约束条件和变分自然条件。
The boundary condition of restriction and the natural condition of variation for the virtual principle of displacement are given too.
本文主要利用拓扑度理论中的不动点定理和变分方法中的极小作用原理及其环绕形式的临界点定理在适当的条件下讨论了一类二阶椭圆边值问题的可解性。
The aim of this thesis is to study the existence of weak solutions for semilinear second order elliptic boundary value problems under suitable conditions through topological and variational methods.
应用变分原理满足其余边界条件并求解应力强度因子。变分方程中只有线积分。
The stress intensity factors are solved by means of variational method to satisfy the other boundary conditions.
研究了一类具有多个变滞量的变系数的二阶中立型差分方程的解的振动性，得到了该类方程振动及其解的一阶差分振动的充分条件。
The oscillation problem for a class of the second order neutral difference equations with several variable delay arguments and variable coefficients was studied.
伴随模式的方法是以数值天气预报的动力模式作为约束条件的变分方法，比传统的变分方法有了很大的改进。
It is a variational method whose constraints are represented by the dynamic model for numerical weather prediction, and is a substantial improvement on the traditional variational scheme.
介绍了三维接触问题的变分原理，推导了接触问题有限元计算公式，讨论了边界接触模式和接触条件。
The variation principle of the 3-D contact problem is introduced, the related formulas based on the finite element method are derived, and the contact mode and condition of the boundary are discussed.
利用有限元离散变分不等原理和基于线性规划余原理的迭代方法，求解自由边值条件下的油膜力。
The oil film forces under free boundary conditions are solved by finite element discrete variational inequalities and iterative method based on complementary principle in linear programming.
应用伴随方法求解以数值预报方程作为约束条件的四维变分资料同化方案，关键问题是如何构造伴随模式。
The key problem of four-dimensional variational data assimilation method, which solves the constraining numerical predict equations through accompanied model, is how to establish an accompanied model.
本文是采用变分估计方法考虑一类椭圆方程在临界指数和自由边界条件下解的存在性问题。
This papar deals with the problem of solution's existence about elliptic equation under limiting exponents and free boundary problem by variational evaluation methods.
应用伴随方法求解以数值预报方程作为约束条件的四维变分资料同化方案 ，关键问题是如何构造伴随模式。
The four-dimensional data assimilation is to integrate the current and past data into a forecast model equation for providing time continuity and dynamic coupling.
研究了一类具有多个变滞量的变系数的二阶中立型差分方程的解的振动性，得到了该类方程振动及其解的一阶差分振动的充分条件。
The oscillation for a class of the second order neutral difference equations with several variable delay arguments and variable coefficients are studied.
研究了一类具有多个变滞量的变系数的二阶中立型差分方程的解的振动性，得到了该类方程振动及其解的一阶差分振动的充分条件。
The oscillation for a class of the second order neutral difference equations with several variable delay arguments and variable coefficients are studied.
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