边值

Nonlinear Riemann boundary value problems and nonlinear Hilbert boundary value problems will be studied in this paper, because they have been researched seldom.

对于非线性的Riemann边值问题和非线性的Hilbert边值问题研究很少，本文试图在这些方面做一些工作。

We consider the existence of positive solutions of second order impulsive boundary value problems by constructing the appropriate homotopy operator and applying the theory of fixed point index in cones. our results contain the conclusion when f ≥ 0 and J_k = 0([6]). Secondly, we discuss multiple positive solutions of the following impulsive boundary

其次，我们在§2.2中讨论了下面的脉冲微分边值问题多正解的存在性在这一部分的讨论中，利用不动点指数理论，在f既非超线性又非次线性的情形下，得到了两个正解的存在性定理，把文[7]的结果推广到脉冲微分边值

Motivated by this, we consider the global behavior of positive solutions of three-point boundary-value problems for second-order differential equations, under two different kinds of boundary-value problems, using fixed point theorem, fixed point index theorem and cone theory.

本文受到文献[7]的启发，运用不动点定理、不动点指数定理以及锥理论，分别研究了两种不同边值条件下二阶微分方程三点边值问题正解的整体性。

In chapter 4, we first discussed the existence of multiple positive solutions of the second order nonsingular Dirichlet boundary value problem for impulsive differential equations by using the fixed point index theorem in cones . Next, we presented some new existence results for singular boundary value problems for second order impulsive differential equations by using fixed point theorem in cones and Leray-Schauder nonlinear alternative theorem.

第四章我们首先利用锥不动点定理讨论了非奇异二阶脉冲微分方程狄利克莱边值问题多个正解的存在性；其次我们用锥不动点定理和Leray-Schauder型非线性抉择定理，讨论了奇异二阶脉冲微分方程狄利克莱边值问题一个及多个正解的存在性。

Special attention should be paid when we apply the decomposition method to two-point boundary value problems, it is necessary to solve a algebraic system;It should be noted that a modification of inverse operator should be made when dealing with singular boundary value problems;Laplace transform and Pade approximants can be coupled to enhance the efficiency of the decomposition method.

比如，在求解两点边值问题时就需要特别注意，这时需要采用待定系数法，最后会涉及到系数方程组的求解；在处理奇异边值问题时需要重新定义逆运算；不少研究人员还把分解方法与Laplace变换和Padé逼近相结合来进一步提高分解方法的精度。

In 2000,Zhou Wenshu gained the existence and uniqueness of the strict convex classical solutions of the third initial-boundary value problems of the Monge - Ampere.

2000年，周文书[10]得到了如下形式的抛物型Monge-Ampère方程的第三初边值问题严格凸古典解的存在唯一性本文的目的是把[10]的结果进行一般性的推广，考虑下列非线性抛物型Hessian方程的第三初边值问题抛物型H。

But most of these papers only considered the nonsingular case...

本章主要内容包括：在§1.1中，我们考虑了如下奇异四阶微分边值问题到目前为止，有关四阶微分边值问题已有不少文献，但大多数文献中作者只讨论了非线性项是非奇异的情形，很少有文献讨论奇异的情形。

The existence of global weak solution for a class of generalized Ginzburg-Landau equations with an inhomogeneous boundary condition was studied. Some integral indentities of smooth solution of inhomogeneous initial boundary value problem of Ginzburg-Landau equations were deduced, by which a priori estimates of the square norm on boundary of normal derivative and the square norm of partial derivatives were obtained.

研究具非线性边界条件的一类广义Ginzburg＿Landau方程解的整体存在性·推导了Ginzburg＿Landau方程的非齐次初边值问题光滑解的几个积分恒等式，由此得到了解的法向导数在边界上的平方模以及解的平方模和导数的平方模估计；通过逼近技巧、先验估计和取极限方法证明了Ginzburg＿Landau方程的非齐次初边值问题整体弱解的存在性

At the beginning of fourth chapter, the article transforms the solving problem of partial differential equation for the American put price into a standard initial and boundary value problem of Parabolic Type by making some transformations.

在第四章，对美式看跌期权价格所满足的偏微分方程定解问题通过作一系列变换，使之转化为一个标准的抛物型初、边值问题，接着又通过傅里叶变换，把抛物型初、边值问题转换为一个关于时间变量的常微分方程初值问题，然后再分别利用改进的欧拉法和有限元法对其进行了求解。

Based on Pontryagin maximum principle,the lunar soft landing problem is transformed into a two-point boundary value problem in mathematics.

首先，从庞德里亚金极大值原理出发，将有限推力作用下月球软着陆问题转化为数学上的两点边值问题；在考虑边界条件及横截条件的前提下，将该两点边值问题转化为针对共轭变量初值和末时刻的优化问题；然后应用非线性规划方法求解所形成的参数优化问题。

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。