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The primary objective of this thesis is to use multigrid method for solving nonseparable elliptic equations with Dirichlet boundary condition on a rectangle. Of course, this method can be applied with any boundary conditions.

这篇论文主要之目的是使用多重网格法来解一些不可分离的椭圆方程式有著Dirichlet条件在矩形的区域上(当然这种方法也可应用在其他的边界条件下)。

We prove the solvability of the first eigenvalue problem for a class of quasilinear elliptic equations including distance potential with homogeneous Dirichlet boundary condition.

变分原理证明了一类含距离位势的拟线性椭圆方程齐次Dirichlet边界条件下第一特征值问题的可解性。

The M Q algorithm has been applied to the second order elliptic problems with the Dirichlet boundary conditions,and the so called R condition is involved in the convergence theorem and the optimal relaxation parameter.

M-Q算法所考虑的是二阶椭圆型Dirichlet边值问题，此时有所谓的R条件成立，算法的收敛定理以及松弛因子的选取都需要该条件。

In chapter 4 and chapter 5, the Dirichlet transmission conditions for overlapping Schwarz methods will be replaced by Robin transmission conditions when applied to general linear elliptic partial differential equations.

为了能够直接应用于某些实际问题，本文第六章把最优Robin参数的确定方法推广到由椭圆型问题离散化得到的稀疏矩阵问题。

The maximum principles for functions which are defined on solutions of semilinear elliptic equations u+f=0(q=|u|~2)subject to Dirichlet boundary conditions u=0 were studied by using Hopf s maximum principle,the estimate of gradient q was obtained.

运用Hopf 极值原理讨论了一类具有Dirichlet边界条件u=0的半线性椭圆方程Δu+f=0(q=|u|2)的解的某个函数的极值原理，利用该结论获得了解的梯度q的估计。

In this paper we study the existence and multiplicity of solutions for the semilinear elliptic Dirichlet problem at the first eigenvalue.

本篇文章主要研究了在一阶共振的半线性椭圆Dirichlet问题解的存在性和多解性，得到了几个解的存在性定理和一个多解性定理。

This paper is devoted to the existence and multiplicity of the solutions of the homogenous Dirichlet problem for a nonlinear singular elliptic equation with natural growth in the gradient.

研究一类具奇性和退化性的非线性椭圆方程Dirichlet问题，通过构造适当的逼近问题并结合紧致方法，证明了解的存在性和多重性。

On Dirichlet Problem of Singular Quasilinear Elliptic Equations;;Mathematics Analysis of Combustion Problem

中文题名奇异拟线性椭圆型方程Dirichlet问题；燃烧问题的数学分析

Many authors posed and discussed some boundary value problems,mainly the Dirichlet problem and mixed boundary value problem for second order elliptic equations with parabolic degeneracy.

许多作者提出和讨论了二阶退化椭圆型方程的一些边值问题，如Dirichlet边值问题和混合边值问题。

This problem is defined as: Given points X, Y on the elliptic curve, find z such that: X = zY The discrete logarithm problem over this group in a finite field is a good one way function because there are currently no known polynomial time attacks forsolving the problem.

这个问题是指：鉴于点X和Y的椭圆曲线，找到这样： X =模糊离散对数问题，这个集团在有限的领域是一个很好的方法之一的功能，因为目前没有任何已知的攻击forsolving多项式时间的问题。

In other research, chondroitin is being investigated for use in several other conditions.

在其它研究，软骨素被调查用於几个其它情况。

They would make fun of him for having to work.

他们拿他的工作来开玩笑。