一般区域上在边界退化的拟线性抛物方程的第—初边值问题

对有界域上拟线性抛物方程第一初边值问题，二阶退化拟线性抛物方程初边值问题已有丰富的成果，可见［１］，［２］，［３］，但对任意域上方程的工作则不多见．在此文中，我们讨论任意区域上在边界退化的拟线性抛物方程初边值问题的存在性．     

具有奇性的常微分方程的边值问题

本文对具有奇性的常微分方程的边值问题（ｔ）ｙ'=(ｔ，ｙ，ｙ＇），ｙ（０）＝ａ，ｙ（１）＝ｂ建立了Ｎａｇｕｍｏ型存在定理．     

Banach空间中N阶脉冲积分-微分方程边值问题的解

运用Monch不动点定理，获得了Banach空间中一类N阶非线性混合型脉冲积分-微分方程边值问题解的存在性．最后给出一个三阶无穷脉冲积分-微分方程边值问题的例子来说明文中所给的条件是合理的．     

含参数的一类奇异边值问题解的结构

该文讨论一类右端含参数λ的奇异常微分方程的边值问题，其中非线性项在无穷远处具有超线性增长性证明，解集含有无界连通分支．     

关于2n阶常微分方程两点边值问题解的存在性与唯一性

本文利用Leray－Schauder度理论建立了一类2n阶非线性常微分方程两点边值问题解的存在性与唯一性定理，以及利用Fredholm择一原理与Fourier展式，建立了一类2n阶线性常微分方程两点边值问题解的存在性唯一性定理．     

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［ｌ，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Ｒｉｅｍａｎｎ－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．     

抽象空间混合型微分-积分方程两点边值问题的解

本文利用混合单调算子理论及Ｍ?ｎｃｈ的一个结果，得到了一类微分方程两点边值问题的解．     

抽象空间混合型微分积分方程两点边值问题的解

本文利用混合单调算子理论及Ｍ¨ｏｎｃｈ的一个结果，得到了一类微分方程两点边值问题的解．     

时滞微分方程的不共轭性

本文推广了共轭点和不共轭微分方程的概念，证明了时滞微分方程的不共轭区间不可能是一个单点集．此外，还证明了时滞微分方程的不共轭性与边值问题的可解性之间的联系．     

一类非经典扩散方程整体解的存在唯一性及长时间行为

本文讨论非经典扩散方程第一初边值问题整体解的存在唯一性及长时间行为，建立了一系列新的结果，较好地改进许多已有的结论．     

New fixed point theorems for mixed monotone operators and local existence-uniqueness of positive solutions for nonlinear boundary value problems

In this article we present a new fixed point theorem for a class of general mixed monotone operators, which extends the existing corresponding results. Moreover, we establish some pleasant properties of nonlinear eigenvalue problems for mixed monotone operators. Based on them the local existence-uniqueness of positive solutions for nonlinear boundary value problems which include Neumann boundary value problems, three-point boundary value problems and elliptic boundary value problems for Lane-Emden-Fowler equations is proved. The theorems for nonlinear boundary value problems obtained here are very general.     

Adjoint and self-adjoint boundary value problems on a geometric graph

We consider boundary value problems of arbitrary order for linear differential equations on a geometric graph. Solutions of boundary value problems are coordinated at the interior vertices of the graph and satisfy given conditions at the boundary vertices. For considered boundary value problems, we construct adjoint boundary value problems and obtain a self-adjointness criterion. We describe the structure of the solution set of homogeneous self-adjoint boundary value problems with alternating coefficients of a differential equation and obtain nondegeneracy conditions for these boundary value problems.     

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．     

一类Riemann-Hilbert边值逆问题

给出解析函数的一类R iem ann-H ilbert边值逆问题的数学提法,依据解析函数R iem ann-H ilbert边值问题的经典理论,讨论了此边值问题的可解性,给出了该边值问题的可解条件和解的表示式.     

一类拟线性边值问题的激波解

本文研究了一类拟线性边值问题的激波解，在适当的条件下，利用微分不等式理论，讨论了原边值问题激波解的存在性和渐近性态。     

一类半线性椭圆型方程奇摄动广义边值问题

讨论了一类非线性椭圆方程奇摄动广义边值问题。在适当的条件下,研究了边值问题广义解的存在、唯一性及其渐近性态。     

Sous-solutions d'équations elliptiques dans L1

We study subsolutions for semilinear elliptic boundary value problems in L1. We consider as well nonlinear as linear boundary conditions. The nonlinear functions may be multivated. We characterize in terms of p.d.e. the subsolutions defined by a nonlinear functional analysis argument. Applications are given to obtain existence results for semilinear elliptic boundary value problems and comparison and estimates for nonlinear parabolic boundary value problems.     

Positive solutions of even order system periodic boundary value problems

We study a class of even order system boundary value problems with periodic boundary conditions. A series of criteria are obtained for the existence of one, two, any arbitrary number, and even a countably infinite number of positive solutions. Criteria for the nonexistence of positive solutions are also derived. As for the second order case, our results extend, improve, and supplement those in the literature for scalar and system boundary value problems. Several examples are given to demonstrate the applications. Moreover, we obtain conditions for system periodic boundary value problems of a different form to have nontrivial solutions by transforming our main results to such problems.     

Overdetermined partial boundary value problems on finite networks

In this study, we define a class of non-self-adjoint boundary value problems on finite networks associated with Schrödinger operators. The novel feature of this study is that no data are prescribed on part of the boundary, whereas both the values of the function and of its normal derivative are given on another part of the boundary. We show that overdetermined partial boundary value problems are crucial for solving inverse boundary value problems on finite networks since they provide the theoretical foundations for the recovery algorithm. We analyze the uniqueness and the existence of solution for overdetermined partial boundary value problems based on the nonsingularity of partial Dirichlet-to-Neumann maps. These maps allow us to determine the value of the solution in the part of the boundary where no data was prescribed. We also execute full conductance recovery for spider networks.