边值

The existence of three positive solutions for boundary value problem of third order differential equation is studied.

证明了几个新的最大值原理，并利用这几个新的最大值原理证明了两类三阶微分方程边值问题解与正解的存在性。

Firstly, the three-dimension boundary question and its corresponding variation question concerning the point-source electrical field on a 3-D structure are presented. Secondly, the finite element method is used to solve the variational equation. The study area is divided into many tetrahedral elements. Then, we interpolate with a tri-linear function in each element. So, the variational equation is converted into a linear equation system. Finally, taking into account saving of time, we make use of symmetric successive overrelaxation preconditioned conjugate gradient algorithm to solve large linear system, and obtain the potential value of each node, resulting in the calculation of the apparent resistivity values on the ground surface.

首先给出了三维构造中点源电场的边值问题以及相应的变分问题；然后利用有限单元法求解变分问题，采用四面体单元对研究区域进行剖分，在单元中进行三线性函数插值，将变分方程化为线性代数方程组；最后，考虑到节约计算时间，利用对称超松弛预条件共轭梯度迭代算法求解大型线性方程组，得到了各节点的电位值，进而计算出地表的视电阻率。

On the base of other researcher, the *** from the basic equations of stable current field to derived the expressions of boundary problems under 3-D condition. Without considering the EM effect and using the generalized variation principle, we can get the corresponding variation equation. Thronging subdivide the 3-D model, interpolation, analysis, and general synthesis with the triangular prism element, we can carry out the simulation on frequency-domain IP\'s parameters under level and undulate topography.

在前人工作的基础上，在忽略电磁效应的情况下，从稳定电流场的基本方程出发，推导了三维区域满足的边值题目，用广义变分原理得到相应的变分题目，通过用三棱柱单元对大地模型进行剖分、插值、总体集成，最后解方程，得到每个节点上的复电位值，最后实现了水平和起伏地形等条件下的激电参数的数值模拟。2。

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。

The aim of this thesis is to study the existence of positive solutions of boundary value problem for nonlinear second order ordinary differential equations , mainly using the fixed point index theory in a cone. The conditions of the existence of positive solutions of the boundary value problem are given in the thesis. We improve the result of the existence of positive solutions either in the sublinear or in the superlinear conditons.

本文主要利用锥上不动点指数定理，解决非线性二阶常微分方程边值问题的正解的存在性问题，并给出了边值问题正解存在的条件，改进了次线性和超线性条件下正解存在的结论。

By using the Krasnoselskii fixed point theorem, an existence result of two positive solutions is obtained under suplinear condition and sublinear condition.

讨论一类四阶非线性微分方程组Dirichlet边值问题正解的存在性，利用Krasnoselskii不动点定理得到这类边值问题在超线性和次线性条件下至少存在两个正解。

In chapter 3,we discuss the existence of solutions for impulsive differential equations with two-point boundary condition.

通过使用脉冲不等式和分析方法，得到了一阶脉冲微分方程周期边值问题新的比较结果，借助所给的新的上下解，结合单调迭代技巧，建立了一阶脉冲微分方程周期边值问题极值解的存在结果。

Based on the upper and lower solutions method,under suitable conditions,existence of solution of a three-point boundary value problem forthird-order ordinary differential equation with nonlinear mixed boundary conditions is obtained.

基于上下解方法，在一定条件下，得到了一类带有非线性混合边界条件的三阶常微分方程的非线性三点边值问题解的存在性，作为上述存在性结果的应用，在推论中给出了一类三阶非线性微分方程三点边值问题解的存在性。

M-point boundary value problem; momotone iterative; equation system; impulsive differential-integro equation; three-point boundary value problem; positive solution; Fixed point; Cone

基础科学，数学，数学分析m点边值问题；单调迭代；方程组；脉冲微积分方程；三点边值问题；正解；不动点；锥

Based upon Adomian decomposition method, we have studied Adomian double decomposition method in this paper. The initial term in Adomian decomposition method has been further decomposed, and modified inverse vector method is obtained.

在求解初边值问题Adomian分解法的基础上，研究了求二维偏微分方程边值问题的双重Adomian分解法，对Adomian分解法的初始项作了进一步分解，使逆算符分解法得到了改进。

Cynanchum Lingtai apricot production in the average weight 65 grams, the brightly-colored fruit, juicy rich, sweet-sour taste, sweet from the nucleolus, when the late Qing Dynasty famous Shaanxi, Gansu provinces, the Qing imperial court Tongzhi tribute for years.

灵台生产的牛心杏平均单果重65克，果实色泽鲜艳，汁多味浓，甜酸适口，离核仁甜，清末时就驰名陕、甘两省，清同治年间曾为朝廷贡品。

Chenopodium album,Solanum nigrum, and Amaranthus retroflexus were very susceptible to the herbicides. Polygonum persicaria and Abutilon theophrasti were relatively less susceptible to the herbicides, and Lycopersicon esculentum was not susceptible to it. The relationship between reduction rates of weed biomass and PPM values of weed leaves 2,4, and 6 days after treatment was established.

供试的6种杂草对该混剂的敏感性存在显著差异：红心藜Chenopodium album、龙葵Solanum nigrum和反枝苋Amaranthus retroflexus对该混剂最敏感，ED90值分别为47.65、71.67和29.17g/hm2；春蓼Polygonum persicaria和苘麻Abutilon theophrasti敏感，ED90值分别为96.91、114.20g/hm2；而番茄不敏感。