一类Dirichlet边值逆问题

给出解析函数的一类Dirichlet边值逆问题的数学提法.依据解析函数Dirichlet边值问题和广义Dirichlet边值问题的理论,讨论了此边值逆问题的可解性.利用解析函数Dirichlet边值问题的Schwarz公式,给出了该边值逆问题的可解条件和解的表示式.     

一类Riemann边值逆问题

本文给出了一类Ｒｉｅｍａｎｎ边值逆问题的正则型与非正则型情况的数学提法和解法     

Riemann边值逆问题与奇异积分方程组

本文给出了一类Ｒｉｅｍａｎｎ边值逆问题的提法及其正则型情况的解法,并利用该Ｒｉｅｍａｎｎ边值逆问题,给出了一类奇异积分方程组的新解法     

一类广义解析函数的Riemann边值逆问题

本文给出了一类有关广义解析函数Riemann边值逆问题的数学提法．在将此边值逆问题转化为边值问题的基础上，借助于广义解析函数边值问题的相关理论，分别获得了此边值逆问题在正则型和非正则型情况下的解．     

上半平面中双周期函数的Hilbert边值逆问题

研究了一类上半平面中双周期函数的Hilbert边值逆问题.利用函数的对称扩张,将其转化为无穷直线上双周期Riemann边值问题,得到了问题的一般解及可解性定理.     

Rimann边值逆问题与奇异积分方程组

本文给出了一类Ｒｉｅｍａｎｎ边值逆问题的提法及其正则型情况的解法。并利用该Ｒｉｅｍａｎｎ边值逆问题,给出了一类奇异积分方程组的新解法。     

实轴上的双解析函数Riemann边值逆问题

提出了一类实轴上的双解析函数Riemann边值逆问题.先消去参变未知函数,再采用易于推广的矩阵形式记法,可把问题转化为两个实轴上的解析函数Riemann边值问题.利用经典的Riemann边值问题理论,讨论了该问题正则型情况的解法,得到了它的可解性定理.     

关于加法逆特征值问题

１．引言 设Ａ（ｃ）＝（ａｉｊ（ｃ））是ｎ阶实矩阵,其元素ａｉｊ（ｃ）（ｉ,ｊ＝１,…,ｎ）是参变量ｃ＝（Ｃ１,…,ｃｎ）Ｔ的实解析函数,λ１（ｃ）,…,λｎ（Ｃ）是矩阵Ａ（ｃ）的特征值,λ１,…,λｎ是给定的实数,代数特征值反问题［４］就是研究如何求解实的ｃ,使Ａ（ｃ）的特征值为给定的λ１,…,λｎ． 假设给定的ｎ个数λ１,…,λｎ互异,且问题的解存在（解不存在时可考虑某种形式的最小二乘解）,过去的研究一般是直接研究或将问题转化为如下等价的非线性方程组 ｄｅｔ（Ａ（ｃ卜人Ｉ）一０, ｉ＝ １,…,…     

一类线性规划逆问题及解法

本文讨论了逆ＬＰ问题的更一般的情况,这里称它为广义逆ＬＰ问题,即在知道了一部分变量和价值系数的条件下,求余下的未知的变量和价值系数,将它们合起来组成给定的ＬＰ问题的最优解。显然若知道全部价值系数就成为ＬＰ问题;若知道全部变量就成为逆ＬＰ问题,它是在根据研制应用软件时提出的。文中给出了解广义逆ＬＰ问题的算法,并成功地用于“宏观经济调控系统”等应用软件的研制中,对要解决的实际问题,给出了强多项式算法。     

一般形式的一阶椭圆型偏微分方程组拟线性Riemann-Hilbert问题

在文[1,2,3]中,E.Wegert和L.V.Wolfersdorf等人讨论了一类全纯函数的拟线性Riemann-Hilbert问题在Hardy空间中的可解性,在文[4]中,讨论了广义解析函数的拟线性Riemann-Hilbert问题,同样得到该边值问题在H2类解空间中的可解性.本文在前面研究工作的基础上,对一般形式的一阶椭圆型偏微分方程组拟线性Riemannn-Hilbert问题作了更深入的讨论,在适当的假设条件下,应用积分算子理论,函数论方法及不动点原理,证明了该边值问题在相应的泛函空间中同样是可解的.     

Moving boundary value problems for the wave equation

We study certain boundary value problems for the one-dimensional wave equation posed in a time-dependent domain. The approach we propose is based on a general transform method for solving boundary value problems for integrable nonlinear PDE in two variables, that has been applied extensively to the study of linear parabolic and elliptic equations. Here we analyse the wave equation as a simple illustrative example to discuss the particular features of this method in the context of linear hyperbolic PDEs, which have not been studied before in this framework.     

Solution of a class of singular boundary value problems

In this work a class of singular ordinary differential equations is considered. These problems arise from many engineering and physics applications such as electro-hydrodynamics and some thermal explosions. Adomian decomposition method is applied to solve these singular boundary value problems. The approximate solution is calculated in the form of series with easily computable components. The method is tested for its efficiency by considering four examples and results are compared with previous known results. Techniques that can be applied to obtain higher accuracy of the present method has also been discussed.     

The forward and inverse problems for a fractional boundary value problem

In this paper, the authors study the forward and inverse problems for a fractional boundary value problem with Dirichlet boundary conditions. The existence and uniqueness of solutions for the forward problem is first proved. Then an inverse source problem is considered.     

Characteristic boundary problems for the Liouville equation

We obtain formulas for solutions of problems with boundary conditions of the 1st, 2nd, and 3rd kind.     

Pseudo almost periodic solutions to parabolic boundary value inverse problems

We first define the pseudo almost periodic functions in a more general setting.Then we show the existence,uniqueness and stability of pseudo almost periodic solutions of parabolic inverse problems for a type of boundary value problems.     

On a class of semipositone discrete boundary value problems

In this paper, we deal with a class of semipositone discrete boundary value problems via critical point theory developed by Chang, and obtain nonexistence and multiplicity results on sublinear nonlinearities and an existence result on superlinear nonlinearities, respectively.     

Polynomial almost periodic solutions for a class of Riemann-Hilbert problems with triangular symbols

Let with α,β∈]0,1[ such that α+β<1, αβ⁻¹∉Q and a,b,c∈C?{0}. In this paper the existence of almost-periodic polynomial (APP) solutions to the equation (with and ) is studied. The natural space in which to seek a solution to the above problem is the space of almost periodic functions with spectrum in the group αZ+βZ+Z. Due to the difficulty in dealing with the problem in that generality, solutions are sought with spectrum in the group αZ+βZ. Several interesting and totally new results are obtained. It is shown that, if 1∉αZ+βZ, no polynomial solutions exist, i.e., almost periodic polynomial solutions exist only if αZ+βZ=αZ+βZ+Z. Keeping to this setting, it is shown that APP solutions exist if and only if the function satisfies the simple spectral condition α+β>1/2. The proof of this result is nontrivial and has a number-theoretic flavour. Explicit formulas for the solution to the above problem are given in the final section of the paper. The derivation of these formulas is to some extent a byproduct of the proof of the result on the existence of APP solutions.     

一类二阶常微分方程无穷多点边值问题多个正解的存在性

研究了一类二阶非线性常微分方程无穷多点边值问题多个正解的存在性,运用不动点指数理论及Holder不等式得到了方程至少存在两个正解的若干充分条件,推广和改进了相关文献的结果.