广义算子半群与广义分布参数系统的适定性

首先,针对广义分布参数系统的求解问题,提出了由Hilbert空间中有界线性算子所引导的广义算子半群和广义积分半群;其次,讨论了广义预解算子的性质、广义算子半群与广义积分半群的性质;最后,研究了广义分布参数系统的适定性问题.     

非线性时变广义分布参数系统的适定性问题

本文的主要目的是讨论非线性时变广义分布参数系统的适定性问题.首先,在Banach空间中引入由连续(可能是非线性的)算子引导的非线性广义发展算子,该非线性广义发展算子是广义发展算子的推广,并研究非线性广义发展算子的性质;然后,应用非线性广义发展算子讨论非线性时变广义分布参数系统的适定性问题,并给出解的构造性表达式.     

广义算子半群的扰动定理

算子扰动问题是研究微分方程的一个重要工具,首先结合Hilbert空间中有界算子引导的广义算子半群的定义研究了广义半群的性质;其次重点讨论了广义算子半群的扰动问题,给出了广义算子半群的加法扰动定理成立的条件.     

一阶广义分布参数系统的极点配置问题

本文讨论了一阶广义分布参数系统的极点配置问题,应用算子的广义逆给出了问题的解及解的构造性表达式.     

一阶广义分布参数系统的极点配置问题

本文讨论了一阶广义分布参数系统的极点配置问题,应用算子的广义逆给出了问题的解及解的构造性表达式．     

广义算子半群的PERRON问题

借助于广义算子半群和广义积分算子半群的关系,讨论广义算子半群的Perron型指数稳定性,研究了广义积分算子半群的渐近行为.     

白噪声分析中广义算子值函数的Bochner-Wick积分

白噪声广义算子在白噪声分析理论及其应用中起着十分重要的作用. 本文主要讨论了白噪声广义算子值函数的积分及相关问题. 主要工作有: 引入了广义算子值测度的概念, 分别讨论了这种测度在象征和算子p-范数意义下的变差及相互关系; 借助于广义算子的Wick积运算, 引入了广义算子值函数关于广义算子值测度的一种积分---Bochner-Wick积分, 讨论了这种积分的性质, 建立了相应的收敛定理并且展示了其在量子白噪声理论中的应用; 探讨了Bochner-Wick积分的Fubini定理及相关问题.     

二阶广义分布参数系统的谱分布

应用泛函分析算子理论的方法研究了Hilbert空间中二阶广义分布参数系统的谱分布问题,利用有界线性算子的广义逆给出了所讨论问题的解及解的构造性表达式。这对研究二阶广义分布参数系统的镇定及渐进稳定性问题都有重要的理论价值。     

一类二阶广义控制系统的反馈控制与极点配置

应用泛函分析及算子理论讨论了Hilbert空间中一类二阶广义控制系统的反馈控制与极点配置问题，利用有界线性算子的广义逆给出了问题有解的一个充分条件，并在此条件下给出了解的构造性表达式，这对广义控制系统的稳定性及渐近稳定性研究具有重要的理论价值．     

一般非均匀凸介质的迁移算子广义本征函数系统的完整性

该文讨论一般非均匀凸介质所确定的迁移算子的广义本征函数系统的完整性问题，利用我们探索的相对收敛方法，完整地刻划了一般非均匀凸介质中迁移问题的广义本征函数系统的完整性问题，我们证明了，对迁移半群E（t），当0∈Pσ（E（t）），迁移算子广义本征函数系统不完整，当0∈Pσ（E（t））时，仅当满足相对收敛条件时，迁移算子的广义本征函数系统完整．     

Hilbert空间中二阶广义分布参数系统的反馈控制与极点配置

应用泛函分析及算子理论方法讨论了Hilbert空间中二阶广义分布参数系统的反馈控制与极点配置问题,通过构造状态反馈的具体形式使所得闭环系统实现无限多个极点的配置;利用有界线性算子的广义逆给出了问题的解及解的构造性表达式;这对广义分布参数系统的极点配置研究具有重要的理论价值.     

二阶耦合广义系统的极点配置问题

讨论了Hilbert空间中二阶耦合广义系统的极点配置问题,应用算子的广义逆给出了问题的解及解的构造性表达式。     

Infinitely many homoclinic solutions for some second order Hamiltonian systems

In this paper, we investigate the existence of infinitely many homoclinic solutions for a class of second order Hamiltonian systems. By using fountain theorem due to Zou, we obtain two new criteria for guaranteeing that second order Hamiltonian systems have infinitely many homoclinic solutions. Recent results in the literature are generalized and significantly improved.     

一类非自治二阶系统的多重周期解

利用广义鞍点定理讨论了一类非自治二阶系统的多重周期解．     

INDECOMPOSABLE INJECTIVE MODULES AND A THEOREM OF KAPLANSKY

Abstract

Every tripotent e of a generalized Jordan triple system of second order uniquely defines a decomposition of the space of the triple into a direct sum of eight components. This decomposition is a generalization of the Peirce decomposition for the Jordan triple system. The relations between components are studied in the case when e is a left unit.     

Periodic solutions of second order non-autonomous Hamiltonian systems with local superquadratic potential

Some existence theorems are obtained for periodic solutions of a class of non-autonomous second order Hamiltonian systems with local superquadratic potential, by making use of the generalized mountain pass theorem.     

Cauchy problem for the generalized Davey-Stewartson systems in Besov spaces and some counterexamples

In this paper, the Cauchy problem of the generalized ellipse-ellipse type Davey-Stewartson systems is discussed. When the dimension of space is greater than or equal to two, we get a unique global solution in Besov spaces by contraction mapping argument. Moreover, by using the F-expansion method, the exact periodic wave solutions for the generalized ellipse-ellipse type Davey-Stewartson systems are discussed, some counter examples are given.     

Connectedness of the Set of Efficient Solutions for Generalized Systems

We introduce the concept of positive proper efficient solutions to the generalized system in this paper. We show that, under some suitable conditions, the set of positive proper efficient solutions is dense in the set of efficient solutions to the generalized system. We discuss also the connectedness of the set of efficient solutions for the generalized system with monotone bifunctions in real locally convex Hausdorff topological vector spaces. This research was partially supported by the National Natural Science Foundation of China (10561007), the Natural Science Foundation of Jiangxi Province, China, and a grant from the National Science Council of ROC.     

Torsion-free path geometries and integrable second order ODE systems

A search for invariants of second order ODE systems under the class of point transformations, which mix the parameter and the dependent variables, uncovers a torsion tensor generalizing part of the curvature tensor of an affine connection. We study the geometry of ODE systems for which this torsion vanishes. These are the ODE systems for which deformations of solutions fixing a point constitute a field of Segré varieties in the tangent bundle of the locally defined space of solutions. Conversely, a field of Segré varieties for which certain differential invariants vanish induces a torsion-free ODE system on the space of solutions to a natural PDE system. The geometry on the solution space is used to produce first integrals for torsion-free ODE systems, given as algebraic invariants of a curvature tensor involving up to fourth derivatives of the equations. In the generic case, there are enough first integrals to solve the equations explicitly in spite of the absence of symmetry. In the case of torsion-free ODE pairs, the field of Segré varieties is equivalent to a half-flat split signature conformal structure, and we characterize in terms of curvature those systems having an abundance of totally geodesic surfaces.