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In chapter four,at first,we investigate classification theory of the positive homogeneous p-Laplacian equation ,the main method is Prufer's transformation,and then we discuss the nontrivial solution for associated nonhomogeneous equation by making use of Leray-Schauder degree.

接着研究了非齐次方程的可解性。在第四章中,我们首先是建立了正齐次p-Laplacian 方程的分类理论,主要利用Prufer 变换。再应用Leray-Schauder 度理论证明非齐次方程的可解性。

In this paper,through construction of an asymptotic solution,We give a necessary condition of the micro local form to local solvability of boundary value problem of pseudo differential equation with two variables.

利用微局部分析的工具,讨论了含两个变量的拟微分方程边值问题的局部可解性;通过构造渐近解的方法,给出了上述问题局部可解的微局部形式的必要条

For the Riemann boundary value problems for the first order elliptic systems , we translates them to equivalent singular integral equations and proves the existence of the solution to the discussed problems under some assumptions by means of generalized analytic function theory , singular integral equation theory , contract principle or generaliezed contract principle ; For the Riemann-Hilbert boundary value problems for the first order elliptic systems , we proves the problems solvable under some assumptions by means of generalized analytic function theory , Cauchy integral formula , function theoretic approaches and fixed point theorem ; the boundary element method for the Riemann-Hilbert boundary value problems for the generalized analytic function , we obtains the boundary integral equations by means of the generalized Cauchy integral formula of the generalized analytic function , introducing Cauchy principal value integration , dispersing the boundary of the area , and we obtains the solution to the problems using the boundary conditions .

对于一阶椭圆型方程组的Riemann边值问题,是通过把它们转化为与原问题等价的奇异积分方程,利用广义解析函数理论、奇异积分方程理论、压缩原理或广义压缩原理,证明在某些假设条件下所讨论问题的解的存在性;对于一阶椭圆型方程组的Riemann-Hilbert边值问题,利用广义解析函数理论、Cauchy积分公式、函数论方法和不动点原理,证明在某些假设条件下所讨论问题的可解性;广义解析函数的Riemann-Hilbert边值问题的边界元方法是利用广义解析函数的广义Cauchy积分公式,引入Cauchy主值积分,通过对区域边界的离散化,得到边界积分方程,再利用边界条件得到问题的解。

In this paper, we will investigate the matrix equation in composition over a complete Brouwerian lattice. First, we give an equivalent condition for the solvability of this equation, i.e. theorem 2.2.3 in this paper: The matrix equation in composition over a complete Brouwerian lattice is solvable iff is the minimal solution of this equation.

本文主要探讨完备Brouwer格上的型矩阵方程,首先给出该类矩阵方程可解的一个等价条件,即本文的定理2.2.3:完备Brouwer格上的型矩阵方程可解的充要条件是是它的解,且是最小解。

The solvability can not be sidestepped, for it relates the problem of equivalence of boundary reduction.

人们在用直接边界元方法进行计算时,并不刻意去考虑积分方程的可解性,但可解性的问题是不能回避的,这涉及到原问题的解与边界积分方程的解的等价性问题。

There are some results for the problem which confine M as only related to λ. In this paper, we break down this confinement and deal with it in a wider situation. By energy estimates and fixed point method, the existence and uniqueness theorem of th...

以前的工作仅在M是参数λ的特殊情况下做的,文中打破了这种限制,在一般情况下讨论了这类非线性双曲方程的可解性,以能量估计与不动点相结合给出了此方程有惟一局部解的存在定理,从而基本上解决了这类方程初值问题的存在惟一性。

On this base,we discuss a class of singular integral equation with Hilbert kernel having solutions with singularity of order one, the solvable conditions for general equation are given and solutions for responding characteristic eq...

在以上工作的基础之上,我们提出了一类不同于文献[13]的解具一阶奇性的Hilbert核奇异积分方程,给出了完全方程的Noether定理和特征方程的解和可解条件。

The direct method of solution for non-normal type of singular integral equation with Hubert kernel is discussed. Their solution have form of integral and the condition of solution have form of the system of equations.

给出了具有Hilbert核非正则型奇异积分方程的直接解法,对核密度函数k在附加某些条件下,得出了方程积分形式的解和方程组形式的可解条件。

Based on the limitation and tightness of computational time, it is concluded that the neighborhood of the equation solution is solvable under the condition of open solvable set.

研究了用差分法求解自治的发展方程时稳定性和收敛性这两个基本概念之间的联系,利用计算时间的有限性和紧致性,在可解集为开集的条件下,得出方程解的邻近也可解的结论。

The Lewy equation is locally solvable and globally solvable,and we have got the analytic expressions of the local solution and the global solution.So we obtain the conclution "when ,Lewy's equation (5) has solution ".

Lewy方程是局部可解与整体可解的,我们已经获得了其局部可微解与整体可微解的解析表达式,获得了"Lewy方程(5)当,则有解"的结论。

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