电报方程双周期解的极大值原理与强正性估计及应用

本文讨论非线性电报方程u_(tt)-u_(xx)+cu_t=F(t,x,u),(t,x)∈R~2时空双2π周期解的存在性。改进了Ortega与Robles-Perez关于线性电报方程双周期解的极大值原理,应用新获得的极大值原理,推广了相应的上下解定理,并且加强了极大值原理的结论,建立了线性方程解的强正性估计,利用这个强正性估计及锥上的不动点定理获得了超线性电报方程及奇异电报方程正双周期解的存在性。     

所有点对之间最快路问题

所有点对之间最快路问题就是要在所有点对(Vs，Vt)之间传送数据δs,t,并找出一条最快的路线．解决所有点对之间最快路问题的关键是产生有效解的等价集合．运用动态点对最短路的算法，本文首先设计了一个时间复杂性为O(mn^2)的产生有效解等价集合的算法，然后研究了静态点对之间最快路问题和动态点对之间最快路问题，其算法的时间复杂性分别为O(mn^2)和O(m^2n^2)．最后本文研究了求和对最小的路问题，证明该问题可以在O(mn^2)时间内解决．     

一类非线性双曲偶合方程组广义解的存在性

本文考虑了具有形式ｎ的弱偶合双曲守恒方程组广义解的存在性问题．极大值原理导出了粘性解Ｌ∞模先验估计，关于单个守恒律简化的补偿列紧方法给出了粘性解的收敛性，即广义解的存在性．     

一类非线性反应扩散方程解的Blow—up问题

本文得用极大值原理研究一类非线性反应扩散方程在各种边界条件下解的Ｂｌｏｗ－ｕｐ问题，给出了整体解不存在的一系列定理，并得到了Ｂｌｏｗ－ｕｐ时间Ｔ的上界。     

一种改进的GDF多目标优化算法

本文提出一种交互式非线性多目标优化算法，该算法是ＧＤＦ多目标优化算法的改进，具有这样的特点：算法采用了既约设计空间策略，具有良好的收敛性；算法生成的迭代点是有效解；算法具有多种一维搜索准则；对于线性多目标问题，算法只需一次交互迭代即可示出多目标问题的最优解。     

含Hardy位势的非线性Schrödinger-Poisson方程正规化解的多重性北大核心CSCD

该文研究了含Hardy位势的非线性Schrödinger-Poisson方程正规化解的多重性问题.首先利用喷泉定理的思想定义了一个极小极大值序列,然后证明这些极小极大值是限制在约束集合上的能量泛函的临界值,从而得到了方程正规化解的多重性,推广了相关文献的结果.     

一类高阶奇异边值问题正解存在的充分必要条件

利用上下解方法和极大值原理给出了一类高阶微分方程的奇异边值问题正解存在的充分必要条件．     

带P-Laplacian算子的四点四阶奇异边值问题的对称正解

本文主要利用上下解方法和Schauder不动点定理,在更广泛的条件下研究了一类带PLaplacian算子的四点四阶奇异边值问题的对称正解的存在性.克服了对非线性微分算子[φp(u″)]″Fredholm抉择定理和极大值原理不能使用的困难,改进并推广了最近的一些已知结果.     

一类四阶次线性奇异边值问题的正解

本文利用极大值原理和通过构造上下解给出了一类四阶次线性微分方程的奇异边值问题有C2[0,1]和C3[0,1]正解存在的充分必要条件.     

一种新的逼近精确罚函数的罚函数及性质

针对可微非线性规划问题提出了一个新的逼近精确罚函数的罚函数形式,给出了近似逼近算法与渐进算法,并证明了近似算法所得序列若有聚点,则必为原问题最优解. 在较弱的假设条件下,证明了算法所得的极小点列有界,且其聚点均为原问题的最优解,并得到在Mangasarian-Fromovitz约束条件下,经过有限次迭代所得的极小点为可行点.     

带转点的三阶常微分方程边值问题的渐近解

研究带转点的三阶常微分方程的边值问题,其中f(x;0)在(-a,b)具有多个多重零点。给出边值问题出现共振的必要条件,求得其一致有效渐近解和余项估计。     

Random problem generation and the computation of efficient extreme points in multiple objective linear programming

This paper looks at the task of computing efficient extreme points in multiple objective linear programming. Vector maximization software is reviewed and the ADBASE solver for computing all efficient extreme points of a multiple objective linear program is described. To create MOLP test problems, models for random problem generation are discussed. In the computational part of the paper, the numbers of efficient extreme points possessed by MOLPs (including multiple objective transportation problems) of different sizes are reported. In addition, the way the utility values of the efficient extreme points might be distributed over the efficient set for different types of utility functions is investigated. Not surprisingly, results show that it should be easier to find good near-optimal solutions with linear utility functions than with, for instance, Tchebycheff types of utility functions.Dedicated to Professor George B. Dantzig on the occasion of his eightieth birthday.     

Global Convergence Analysis of Algorithms for Finding Feasible Points in Norm-Relaxed MFD

This paper introduces two new algorithms for finding initial feasible points from initial infeasible points for the recently developed norm-relaxed method of feasible directions (MFD). Their global convergence is analyzed. The theoretical results show that both methods are globally convergent; one of them guarantees finding a feasible point in a finite number of steps. These two methods are very convenient to implement in the norm-relaxed MFD. Numerical experiments are carried out to demonstrate their performance on some classical test problems and to compare them with the traditional method of phase I problems. The numerical results show that the methods proposed in this paper are more effective than the method of phase I problems in the norm-relaxed MFD. Hence, they can be used for finding initial feasible points for other MFD algorithms and other nonlinear programming methods.     

序Banach空间非混合单调二元算子不动点的存在唯一性及应用

利用锥理论和Banach压缩映象原理在更一般的条件下建立了序Banach空间中一类非混合单调二元算子不动点的存在唯一性定理,并应用到Banach空间中二阶非线性Volterra型微分-积分方程初值问题,改进并推广了已有的一些结果.     

On the determination of boundary collocation points for solving some problems for the Laplace operator

Boundary collocation is a method for obtaining approximate solutions of boundary problems for linear partial differential equations, for which complete families of particular solutions are explicitly known. The method contains various decisions which are important for its performance, such as choice of solution subspace, choice of basis for the subspace, and choice of collocation points. Using a model problem, some particular strategies for the determination of collocation points are investigated.     

亚纯函数系数高阶复域微分方程解的不动点

研究了一类亚纯函数系数的高阶线性微分方程的解的不动点问题,应用值分布的理论和方法,得到了复域微分方程亚纯解的不动点性质.     

单参数非线性问题中高阶奇异点的计算

本文考虑计算单参数非线性问题中高阶奇异点的数值方法，基于确定奇异点的一个普适的扩张系统，结合同伦参数的拟弧长延拓，给出了计算各类高阶奇异点的一个统一算法，数值例子表明了算法的有效性．     

Critical points and positive solutions of singular elliptic boundary value problems

Usually we do not think there is variational structure for singular elliptic boundary value problems, so it cannot be considered by using critical points theory. In this paper, we use critical theory on certain convex closed sets to solve positive solutions for singular elliptic boundary value problems, especially use the ordinary differential equation theory of Banach spaces to obtain new results on the existence of multiple positive solutions. The method is useful for other singular problems.     

Compromise solutions and estimation of the noninferior set

A general framework is presented in which the relation of the set of noninferior points and the set of compromise solutions is studied. It is shown that the set of compromise solutions is dense in the set of noninferior points and that each compromise solution is properly noninferior. Also, under convexity of the criteria space, a characterization of the properly noninferior points in terms of the compromise solutions is presented. In this characterization, the compromise solutions depend continuously on the weights. Use of the maximum norm is studied also. It is shown that a subset of these max-norm solutions, obtained by taking certain limits of compromise solutions, is dense and contained in the closure of the set of noninferior points.     

EXISTENCE THEOREM AND FINITE ELEMENT METHOD FOR STATIC PROBLEMS OF A CLASS OF NONLINEAR HYPERELASTIC SHELLS

In this paper, various boundary value problems of hyperelastic shells are considered. It is assumed that the storede-nergy function W(x, F) of the material,of which the shell is made, satisfies polyconvex conditions proposed by Ball~([2]).Existence of minimum points of the total energy of the shell in suitably chosen function spaces, and in suitably chosen finite element spaces is proved. Convergence of the finite element solutions is proved under certain regular conditions on the minimum points and some additional assumptions on W(x, F). A Gradient type computing scheme for solving the finite element solutions is given, and global convergent result is obtained.