微分方程的积分

Then by using the Riemann's function of the operator and constructing an auxiliary problem, an integrodifferential equation equivalent to former problem is got.

然后利用该算子的Riemann函数，通过构造辅助问题，得到了一个等价积分微分方程。

Now we study the properties of four multi-layer potentials and their high deriva-tives of biharmonic equation in the plane when they approach the boundary of adomain.

我们研究了重调和方程四种多层位势及其高阶微商在边界附近的性质，得到了这些微商新的表达式，从而将重调和方程的自由边值问题归化为新的边界积分-微分方程组。

Later, the molecular beam experiments show that the distribution of these two laws are correct .1872, he is also given the basic equation of kinetic theory of gases - Boltzmann integro-differential equations.

后来的分子束实验证明，这两个分布律都是正确的。1872年，他又给出气体动理论的基本方程——玻耳兹曼积分微分方程。

The proposed scheme is developed using the local coordinate system based PML splitting equations and integral approaches of the PML equations under a discretization of triangular grid cells.

本方法的核心是建立局部坐标系下的分裂方程和基于积分近似的微分方程弱形式。

The theory of maximal monotone operator is one of the most importance successes in the area of nonlinear analysis. It provides a powerful general framework for the study of nonlinear partial differential equations, nonlinear integral equations, control theory, optimization. Practically, it has be applied abroad in physics, economics and engineering.

极大单调算子理论是非线性分析领域的有效工具之一，已被广泛应用于非线性偏微分方程、非线性积分方程、控制论、最优化理论等学科，在物理学、经济学、工程学等应用学科也有着广泛的应用。

Secondly, point out that meshless method is different from finite element method in handling boundary condition and numerical integral because the approximation function of meshless method is not inserted function, it have itself special methods. Deduces meshless Galerkin essential equation of parabolic partial differential equation with the method ofweighted residuals------Galerkin. Furthermore, discusses the main factors which may effectthe calculation precision and give some suggestion with which can get the best result.

其次，由于无网格法的近似函数不是插值函数，所以无网格Galerkin法在处理边界条件和对区域积分时是不同于有限元的，它有其独特的处理方法，从加权残量法——Galerkin出发，推导出抛物型偏微分方程无网格Galerkin法的基本方程，并对影响无网格Galerkin法的主要因素进行探讨，给出了取得最佳效果的相应建议。

According to the plane cross section assumption, configuration of a rod is expressed as a history of the cross section with arc coordinate. A special solution which stands for equilibrium in straight line state is obtained from differential equilibrium equation. Linear perturbation equation is derived and its general solution is obtained in which the integral constants are determined by constrained conditions at two ends of the rod. The condition of existence of non zero solution of the integral constants gives to the Greenhill formula of exact elastic rod model, which shows that the boundary of stable area is a closed curve and of symmetry, and inference of shearable and extensible to stability of the rod is depend on three factors: difference between flexibility of shear and extension of a section of the rod, bending stiffness and the length of the rod.

基于平面截面假定，弹性杆的位形表达为截面的弧坐标历程，根据平衡微分方程得到了两端受力螺旋作用时的直线平衡特解，导出了线性化扰动方程及其通解，积分常数根据两端铰支时的边界条件确定，并根据其存在非零解的条件得到弹性直杆精确模型的Greenhill公式，表明稳定域为一对称的封闭区域，拉/压和剪切对稳定性的影响取决于：拉/压柔度与剪切柔度之差，抗弯刚度和杆长这三个因素

This article investigates the two-point boundary value problem to a coupled system of nonlinear fractional differential equations. By applying growth conditions on the nonlinear terms, we obtain an existence result of solutions. Our analysis relies on the Schauder fixed-point theorem and the reduction of the considered problem to the equivalent coupled system of integral equations.

本文讨论非线性分数阶微分方程耦合系统的两点边值问题，应用Green函数，将其转化为等价的积分方程耦合系统，并设非线性项在无穷远处有增长条件，应用Schauder不动点定理证明解而非限于正解的存在性。

By the properties of k-th order symmetric function , we obtained some estimations of integral mean value of the solutions of the boundary value problems for some kind of special partial differential equations in Dk which can be changed into Laplace equations in the unit circle by way of suitable transform .

另外，D_k上的某一类特殊的偏微分方程经过适当变换后转化为单位圆上的Laplace方程，其边值问题的解的积分平均估计可由k次对称化函数的性质较好给出。

In chapter 2, By combining the theory of exponential dichotomies of linear system and the method of functional analysis, some sufficient conditions that guarantee the existence and uniqueness of periodic solution of the systems are obtained.

第四章，考虑具有无穷时滞的非线性积分微分方程概周期解的存在性和唯一性问题，利用矩阵测度和不动点方法获得了一类方程的概周期解的存在性与唯一性的充分条件。

Plunder melds and run with this jewel!

掠夺melds和运行与此宝石！

My dream is to be a crazy growing tree and extend at the edge between the city and the forest.

此刻，也许正是在通往天国的路上，我体验着这白色的晕旋。