抽象半线性发展方程的正解及应用

本文讨论了有序Ｂａｎａｃｈ空间中的正算子半群的特征，把通常常微分方程及偏微分方程的上、下解方法引入到有序Ｂａｎａｃｈ空间中的半线性发展方程，获得了整体解与正解的存在性．     

Banach空间非线性Sturm-Liouville问题的正解

本文提出一种新的描述常微分方程右端项非线性的方法，得到了Ｂａｎａｃｈ空间 Ｓｔｕｒｍ－Ｌｉｏｕｖｉｌｌｅ问题正解的存在性．     

Banach空间中非线性脉冲积分微分方程的正解

借助于锥理论，本文讨论Ｂａｎａｃｈ空间中非线性脉冲积分微分方程的解，给出一阶脉冲微分方程存在唯一正解的条件及混合型脉冲积分微分方程至少具有两解的条件。     

Banach空间泛函微分方程的正解

本文利用锥理论研究Ｂａｎａｃｈ空间泛函微分方程正解的存在性,在紧型条件下获得一个新结果。     

一类微分方程组的多重正解

本文讨论了 Ｂａｎａｃｈ空间中 Ｓｔｕｒｍ－Ｌｉｏｕｖｉｌｌｅ问题正解的存在性与多解性，通过线性算子的谱半径，给出其正解存在与多解的条件．     

Banach空间中一类带奇异性的脉冲微分方程边值问题的正解

利用锥理论和Ｍ¨ｏｎｃｈ不动点定理，讨论了Ｂａｎａｃｈ空间中一类带奇异性的脉冲微分方程边值问题正解的存在性．作为其应用，给出了一个例子．     

Banach空间常微分方程理论的若干问题

本文综述了Ｂａｎａｃｈ空间常微分方程理论近期的发展，主要为紧型条件，耗散型条件，非线性半群、上下解方法，边值问题、Ｂａｎａｃｈ空间中的积－微分方程和脉冲方程，以及对于不动点理论和临界理论的应用，并且给出了作者们在这一领域中的一些新结果。     

非线性算子方程迭代解的存在性定理及其应用

在Ｂａｎａｃｈ空间中,利用锥理论和单调迭代方法研究了一类非线性算子方程的解和最小最大耦合解的存在与迭代逼近定理,并应用到Ｂａｎａｃｈ空间中非线性Ｖｏｌｔｅｒｒａ型积分方程和常微分方程的初值问题．     

算子值加权模式在Banach空间的实现理论

本文处理能在Ｂａｎａｃｈ空间中实现的线性连续时间系统．这里，输入、输出和状态空间都是无穷维Ｂａｎａｃｈ空间．我们证明：加权模式有Ｂａｎａｃｈ空间实现的充要条件是它强连续且为指数阶．对状态算子是解析半群的无穷小生成元的情况，得到了Ｂａｎａｃｈ空间实现的存在性定理．所有定理都是在时间域中给出的．     

Banach空间半线性发展方程的周期解

把上、下解方法引入到有序Ｂａｎａｃｈ空间中的半线性发展方程周期解问题，利用正算子半群特征与单调迭代程序，获得了最大周期解与最小周期解的存在性．所得的结果概括和推广了常微分方程与偏微分方程中的有关结论     

Existence of nontrivial solutions for superlinear three-point boundary value problems

In this paper, we investigate the existence of nontrivial solutions for some superlinear second order three-point boundary value problems by applying new fixed point theorems in ordered Banach spaces with the lattice structure derived by Sun and Liu.     

Banach空间非线性Sturm-Liouville边值问题的正解

通过对非紧性测度的精细计算, 结合相应的线性方程的特征值理论, 运用凝聚映射的不动点指数理论, 分别在超线性与次线性情形下, 讨论Banach空间Sturm-Liouville边值问题正解的存在性.     

A Semilocal Convergence of a Secant–Type Method for Solving Generalized Equations

In this paper we present a study of the existence and the convergence of a secant–type method for solving abstract generalized equations in Banach spaces. With different assumptions for divided differences, we obtain a procedure that have superlinear convergence. This study follows the recent results of semilocal convergence related to the resolution of nonlinear equations (see [11])     

Smoothing Newton method for operator equations in Banach spaces

In this paper, the global and superlinear convergence of smoothing Newton method for solving nonsmooth operator equations in Banach spaces are shown. The feature of smoothing Newton method is to use a smooth function to approximate the nonsmooth mapping. Under suitable assumptions, we prove that the smoothing Newton method is superlinearly convergent. As an application, we use the smoothing Newton method to solve a constrained optimal control problem.     

Sign-Changing Solutions and Multiple Solutions Theorems for Semilinear Elliptic Boundary Value Problems with a Reaction Term Nonzero at Zero

In this paper, we use the ordinary differential equation theory of Banach spaces and minimax theory, in particular, the local mountain pass lemma to study asymptotically linear and superlinear elliptic boundary value problems with a reaction term nonzero at zero, and get new multiple solutions and sign-changing solutions theorems. Moreover, the sign-changing solutions change sign exactly once under some conditions.     

The Lagrange-Newton method for state constrained optimal control problems

Local convergence of the Lagrange-Newton method for optimization problems with two-norm discrepancy in abstract Banach spaces is investigated. Based on stability analysis of optimization problems with two-norm discrepancy, sufficient conditions for local superlinear convergence are derived. The abstract results are applied to optimal control problems for nonlinear ordinary differential equations subject to control and state constraints.This research was completed while the second author was a visitor at the University of Bayreuth, Germany, supported by grant No. CIPA3510CT920789 from the Commission of the European Communities.     

Lorentz序列空间的装球问题

Ｂａｎａｃｈ空间中装球问题的研究，近四十年来已取得了令人瞩目的发展。Ｂａｎａｃｈ空间的装球值的范围已经确定，Ｌ＿ｐ空间及Ｏｒｌｉｃｚ序列空间Ｉ＿Ｍ等许多经典Ｂａｎａｃｈ空间装球值已经找到．本文研究又一类经典Ｂａｎａｃｈ空间──Ｌｏｒｅｎｔｚ序列空间的装球问题，给出了Ｌｏｒｅｎｔｚ序列空间的装球值。     

次可分与拟可分的Banach空间

Ｘ是Ｂａｎａｃｈ空间，对Ｘ的每一弱可分且弱紧的子集Ｋ，若（ｋ，ω）可度量，则称Ｘ是次可分的。如果对任意的可分，则称Ｘ是拟可分的。本文证明了这两类新引入的空间比可分空间与弱紧生成的Ｂａｎａｃｈ空间都要广泛并且保留了可分空间的许多重要性质。     

Fixed point theorems for a class of nonlinear mappings related to maximal monotone operators in Banach spaces

In this paper, the class of nonspreading mappings in Banach spaces is introduced. This class contains the recently introduced class of firmly nonexpansive type mappings in Banach spaces and the class of firmly nonexpansive mappings in Hilbert spaces. Among other things, we obtain a fixed point theorem for a single nonspreading mapping in Banach spaces. Using this result, we also obtain a common fixed point theorem for a commutative family of nonspreading mappings in Banach spaces. Received: 10 August 2007     

Weak and Strong Convergence Theorems for New Demimetric Mappings and the Split Common Fixed Point Problem in Banach Spaces

In this paper, we consider the split common fixed point problem for new demimetric mappings in Banach spaces. Using the idea of Mann’s iteration, we prove a weak convergence theorem for finding a solution of the split common fixed point problem in Banach spaces. Furthermore, using the idea of Halpern’s iteration, we obtain a strong convergence theorem for finding a solution of the problem in Banach spaces. Using these results, we obtain well-known and new weak and strong convergence theorems in Hilbert spaces and Banach spaces.