一维p-Laplacian方程边值问题多解的存在性

利用Clark定理，研究了一维p-Laplacian方程边值问题多解的存在性，得到了这类边值问题至少有n对非平凡解的充分条件．     

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。     

一类具有非局部反应扩散方程的奇摄动问题

本文讨论一类具非局部反应扩散方程的奇摄动初始边值问题，利用迭代法及微分不等式，研究了初始边值问题的存在唯一及其渐近性态。     

关于奇异二阶微分方程（Φ（X’））’＋f（t，X）＝0的某些可解准则

本文讨论了一类右端具有奇异性的二阶常微分方程的边值问题，证明了当ｆ（ｔ，ｘ）关于ｔ的奇异程度大于某值时，边值问题无解，而当奇异程度小于某值时，边值问题有解．关于ｕ在ｕ＝０的奇异程度没有限制．     

非线性四阶方程正解存在问题

本文讨论了一个四阶非线性方程在二类不同边界条件下正解的存在问题，即多点边值问题和积分型的边值问题．采用的方法是锥拉伸和压缩不动点定理，这里的结果推广了这类四阶方程边值问题的结果．     

平面弹性力学中带孔洞的自由边界含裂纹问题

本文在文献「１」、「２」的基础上提出了一类平面弹性力学中带多边形孔洞的自由边界含裂纹问题，我们先将其分解为一个解析函数的黎曼－希尔伯特边值问题和一个复方程的混合边值问题，然后利用边值问题的理论和方法，讨论了这个问题的可解性。     

主算子具非平凡核的抽象边值问题的适定性

本研究主算子具非平凡核时抽象边值问题的适定性问题，在较为一般的条件下，我们证明了抽象边值问题是适定的。我们还研究了无穷远处边界条件的改变引起抽象边值问题的出现多解问题，并就两种不同的无穷远处边界条件讨论了方程的多解。     

二阶常微分方程及Thomas—Fermi方程的边值问题

本文利用上、下解方法推广了Ｍ．Ｌｅｅｓ关于半线性边值问题的结果，给出了另一类边值问题解的存在唯一性的一个充分条件；并利用所得的结果证明了Ｔｈｏｍａｓ－Ｆｅｒｍｉ方程的边值问题解的存在唯一性，从而推广了Ｃ．Ｄ．Ｌｕｎｉｎｇ的结果。     

偏微分方程的函数论方法及应用和计算

本文主要介绍了偏微分方程一些边值问题的函数论方法。首先给出了边值问题的适定提法；其次研究了多复变函数、Ｃｌｉｆｆｏｒｄ代数、某类抛物型方程、一些复合型方程组和双曲型方程组各种边值问题的可解性；进而使用一阶椭圆型方程组间断边值问题的结果，解决了渗流理论、空气动力学与弹性力学中提出的若干自由边界问题；最后还讨论了某些椭圆边值问题与拟共形映射的近似解法。从此文可以看出；函数论方法在处理偏微分方程的一些优     

一类非线性泛函边值问题的可解性

本文考虑非线性泛函边值问题，利用Ｂｏｒｓｕｋ定理与Ｌｅｒａｙ－Ｓｃｈａｕｄｅｒ不动点定理，得到了上述边值问题的若干可解性结果。     

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.     

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.     

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．     

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.     

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.     

具有非局部边界条件的奇摄动反应扩散问题

本文研究了一类具有非局部边界条件的奇摄动反应扩散初始边值问题．在适当的条件下，利用比较定理讨论了问题解的渐近性态．     

Linear and nonlinear degenerate boundary value problems in Besov spaces

The boundary value problems for linear and nonlinear degenerate differential-operator equations in Banach-valued Besov spaces are studied. Several conditions for the separability of linear elliptic problems are given. Moreover, the positivity and the analytic semigroup properties of associated differential operators are obtained. By using these results, the maximal regularity of degenerate boundary value problems for nonlinear differential-operator equations is derived. As applications, boundary value problems for infinite systems of degenerate equations in Besov spaces are studied.     

椭圆型方程的内层和边界层渐近解

本文讨论了一类半线性椭圆型方程边值问题.利用微分不等式理论,研究了边值问题内层和边界层解的存在性和渐近性态.     

Noncoercive Boundary Value Problems for Elliptic Partial Differential and Differential-Operator Equations

In this paper we find conditions guarantee that irregular boundary value problems for elliptic differential-operator equations of the second order in an interval are fredholm. We apply this result to find some algebraic conditions guarantee that irregular boundary value problems for elliptic partial differential equations of the second order in cylindrical domains are fredholm. Apparently this is the first paper where the regularity of an elliptic boundary value problem is not satisfied on a manifold of the dimension equal to dimension of the boundary. Nevertheless the problem is fredholm and the resolvent is compact. It is interesting to note that the considered boundary value problems for elliptic equations in a cylinder being with separating variables are noncoercive.