非线性算子的渐近歧点

利用拓扑度方法作为主要工具研究Banach空间中非线性算子的渐近歧点的存在性,但并没有假定非线性算子是渐近线性算子.最后,把一般结果应用于常微分方程的Sturm-Liouville问题.     

奇点处分岔解支的数目问题*

本文在孤立奇点的假设下证明了带参数非线性方程组解的孤立性,同时指出在分岔点处必有而且仅有有限条解支分岔出来．这一结论是分岔问题数值方法的一个理论基础．     

包含极值点和分枝点的解曲线跟踪算法的摄动解法

本文提出了采用摄动格式求解非线性方程组的解曲线跟踪算法的计算格式.文中着重讨论了解曲线上非正则点的搜索,以及从这些非正则点——转向点或分枝点——继续跟踪超临界平衡路径的计算方法.文中把这一算法应用于弹性薄壳的屈曲分析。通过柱壳和环壳的算例得到它们的整个屈曲过程的平衡路径和变形形态.     

Takens—Bogdanov分岐点的分裂迭代算法

本文构造分裂迭代算法用于计算Takens-Bogdanov分岐点,该方法将减少计算的工作量和占用的内存,可以调节的速度线性收敛,并且可以求得Takens-Bogdanov分岐点处fx^及fx^0的广义零特征向量,数值计算说明了算法的有效性。     

一类Hammerstein积分方程的正分歧点

本文考虑有序Banach空间中形如x(t)=∫_Gk(t,s)[λAx(s) f(s,x(s),λ)]ds的Hammerstein型积分方程,给出了此类方程存在正分歧点的某些充分条件。     

Hilbert空间中非扩张映象的最近的公共不动点的逼近问题

本文在Hilbert空间的框架下,研究无限族非扩张映象T_1,T_2,…的迭代程序x_n+1=λ_(n+1)y+(1-λ_(n+1))T_(n+1)x_n的收敛性问题．在适当的条件下,证明了该迭代序列收敛于这一非扩张映象族的最近的公共不动点．其结果改进和推广了引文中相应的结果．     

Homotopical Stability of Isolated Critical Points of Continuous Functionals

We give a simple proof of the so-called Potential well theorem of Ioffe and Schwartzman, estimating the size of the potential well associated with a local minimum of a continuous functional defined on a complete metric space. Applications to the homotopical stability of an isolated local minimum and to an abstract bifurcation result, as in Ioffe and Schwartzman, are described. We also establish a result on homotopical stability of arbitrary isolated critical points of continuous functionals, thus extending a result of Chang.     

一类反应扩散方程的分歧

本文讨论了一类反应扩散方程的分歧现象.运用所谓基于李雅普诺夫施密特约化的奇异理论方法,得到了满意的结果.     

一种计算Hopf分歧点的新方法

构造一种新的方法计算Hopf分歧点.这种方法构造了小扩张系统,从而减少了计算量并节约了内存.数值例子的计算说明了方法的有效性.     

带有多个分歧参数的等变分歧问题的万有开折

对于含一个分歧参数的分歧问题,已有万有开折定理阻［１,２］．本文考虑带有多个分歧参数的等变分歧问题,并且允许它的状态空间与靶空间可以不同,给出了等变万有开折定理的更一般的形式,［１,２］中相关结果其特殊情形．     

Voronoi Diagrams of Real Algebraic Sets

A collection of n (possibly singular) semi-algebraic sets in ^d of dimension d–1, each defined by polynomials of maximal degree , has ((n) ^d ) first-order Voronoi cells (for any fixed d). In the nonhypersurface case, where the maximal dimension of the semi-algebraic sets is m d–2, the number of first-order Voronoi cells is bounded above by O(n ^{m+1 d} ) (for nonsingular semi-algebraic sets) or by O((n) ^d ) (in general). The complexity of the entire kth-order Voronoi diagram of a generic collection of n non-singular real algebraic sets in R ^d of maximal dimension m<d and maximal degree is O(n ^{min(d+k,2d)2(m+1)d} ).     

Banach空间中广义平衡问题和一族相对非扩张映象的强收敛定理

在Banach空间中,用收缩投影的方法证明了广义平衡问题和一族相对非扩张映象的公共不动点的强收敛定理.结论改进了最近一些人的研究结果     

The Stability and Hopf Bifurcation of the Prey-predator System with Delay and Migration

In this paper we first investigate the system with the inftuence of delay and migration and give a theoretical analysis of the alternative change of the stability discovered by Stepan with computer program, then we reduce the system with the center manifold theorem and present an approximation form of Hopf bifurcation solutions. Finally we give the numerical analysis of stability for a concrete periodic solution.     

Perestroikas of Convexified Apparent Contours and Global Phase Diagrams in Thermodynamics

We obtain the classification of singularities occurring in families of convex hulls of apparent contours up to codimension 3. The results for codimension 2 singularities allow us to supplement Varchenko's classification of local singularities of thermodynamic phase diagrams of binary mixtures. Singularities of three-parameter families specify so-called global phase diagrams in three-dimensional parameter spaces and define all local perestroikas of phase diagrams in generic one-parameter families of binary mixtures.     

一类捕食与被捕食系统的稳定性与分岔分析

本文利用Schur—Cohn—Jury引理及分岔理论讨论了一类捕食与被捕食系统的动力学性质，分析了其正平衡点的稳定性，并讨论了Neimark—Sacker分岔稳定性与方向。通过数值模拟验证了所得结果的正确性。     

一类半圆形弹性杆大变形的多解性与分支

研究一端固定,另一端自由且在其中间受一竖直向下的集中力,自由端受一水平向左的集中力的平面半圆形弹性杆的大变形.通过建立相应的数学模型,利用流形法画出模型解的分支图,进而分析系统的分支特性和多解性,并得到变形后弹性杆的形状.     

一类捕食者-食饵模型的稳定性及Hopf分支

研究一类具有时滞和阶段结构的捕食模型的稳定性和Hopf分支.以滞量为参数,得到了系统正平衡点的稳定性和Hopf分支存在的充分条件.利用规范型和中心流形定理,给出了确定Hopf分支方向和分支周期解的稳定性的计算公式.     

关于Shimoji and Takahashi一个定理的简单证明

目的是在一般Banach空间中建立一个无限可数多个非扩张映像族的公共不动点的强收敛定理．使用一些新的分析技巧,尤其是Dotson引理和W映像技巧,给出了Shimoji and Takahashi的一个定理的简单证明．     

一类弹性储液箱同液体耦合晃动问题的分岔行为分析

建立了弹性圆柱型储液箱同液体耦合系统在外激励下的非线性振动方程组．采用多尺度法、奇异性理论研究此非线性振动系统共振解的分岔行为,通过对其分岔行为的分析和讨论,得到了这一系统的多种转迁集和分岔图,建立了系统参数与其拓扑分岔解的联系,并且分析了不同参数下系统的分岔特性,为实现储液器参数的优化控制提供了理论依据．     

On the Number of Unbounded Solution Branches in a Neighborhood of an Asymptotic Bifurcation Point

We suggest a method for studying asymptotically linear vector fields with a parameter. The method permits one to prove theorems on asymptotic bifurcation points (bifurcation points at infinity) for the case of double degeneration of the principal linear part. We single out a class of fields that have more than two unbounded branches of singular points in a neighborhood of a bifurcation point. Some applications of the general theorems to bifurcations of periodic solutions and subharmonics as well as to the two-point boundary value problem are given.