The study of traffic equilibrium problems with capacity constraints of arcs

In this paper, we study traffic equilibrium problems with capacity constraints of arcs and derive a sufficient condition of weak vector equilibrium flows. Based on this sufficient condition, we establish the existence and essential components of the solution set for traffic equilibrium problems with capacity constraints of arcs.     

带梯度吸收项的快扩散方程的自相似奇性解

研究一类带有非线性梯度吸收项的快速扩散方程的自相似奇性解．通过自相似变换,该自相似奇性解满足一个非线性常微分方程的边值问题,再利用打靶法技巧研究该常微分方程初值问题解的存在唯一性并根据初值的取值范围对其解进行了分类．通过对这些解类的性质的分析研究,得出了自相似强奇性解存在唯一性的充分必要条件,此时自相似奇性解就是强奇性解．     

Existence of optimal open-loop strategies for a class of differential games

In this paper, the class of differential games with linear system equations and a quadratic performance index is investigated for saddlepoint solutions when one or both of the players use open-loop control. For each formulation of the game, a necessary and sufficient condition is obtained for the existence of an optimal strategy pair that generates a regular optimal path. For those cases where a solution exists, the unique saddle-point solution is presented. Also, relationships are established between the time intervals of existence of solutions for the various formulations of the game.This research was supported by the National Science Foundation, Grant No. GK-3341.     

A singular solution with smooth initial data for a semilinear parabolic equation

We consider the Cauchy problem for a parabolic partial differential equation with a power nonlinearity. Our concern in this paper is the existence of a singular solution with smooth initial data. By using the Haraux-Weissler equation, it is shown that there exist singular forward self-similar solutions. Using this result, we also obtain a sufficient condition for the singular solution with general initial data including smooth initial data.     

二阶脉冲微分方程三点边值问题正解的存在性

利用混合单调算子的不动点定理讨论了一类二阶奇异脉冲微分方程三点边值问题,得到了正解存在的一个充分条件.     

负指数的脉冲EMDEN—FOWLER方程奇异边值问题的正解

利用不动点定理得到了脉冲奇异混合边值问题的上下解方法，并且利用此方法得到了负指数的脉冲Emden—Fowler方程奇异混合边值问题正解存在的充分必要条件．     

负指数的脉冲EMDEN-FOWLER方程奇异边值问题的正解

利用不动点定理得到了脉冲奇异混合边值问题的上下解方法,并且利用此方法得到了负指数的脉冲Emden-Fowler方程奇异混合边值问题正解存在的充分必要条件.     

Positive solutions of superlinear semipositone singular Dirichlet boundary value problems

In this paper, we study a class of superlinear semipositone singular second order Dirichlet boundary value problem. A sufficient condition for the existence of positive solution is obtained under the more simple assumptions.     

一类二阶奇异微分方程正解的存在唯一性

利用上下解方法,不动点理论研究奇异微分方程u" f(t,u)=0,t∈(0,1)在边界条件au(0)-βu'(0)=0,γu(1) δu'(1)=0下C[0,1]正解和C1[0,1]正解的存在性与唯一性.其中非线性项f(t,u)关于u是减的,仅满足较弱的要求.     

A necessary and sufficient condition of existence of positive solutions for nonlinear singular differential systems

In this paper, by means of monotone iterative technique, a necessary and sufficient condition of the existence of positive solution for a class of nonlinear singular differential system is established, the results of the existence and uniqueness of the positive solution and the iterative sequence of solution are given. In the end, two classes extending boundary value differential systems are discussed and some further results are obtained.     

四阶奇异边值问题的正解

该文利用锥不动点理论，分别给出了超线性四阶微分方程奇异边值问题正解存在的充分条件和充分必要条件.     

Existence of solutions of boundary value problems for singular fractional <Emphasis Type="Italic">q</Emphasis>-difference equations

In this paper, we study the existence and uniqueness of solutions for a class of singular three-point boundary value problems of fractional q-difference equations invovling fractional q-derivative of Riemann–Liouville type. Based on the generalization of Banach contraction principle, we obtain a sufficient condition for existence and uniqueness of solutions of the problem. By applying the Krasnoselskii’s fixed point theorem, we establish a sufficient condition for the existence of at least one solution of the problem. As applications, two examples are presented to illustrate our main results.     

Necessary and sufficient condition for the existence of positive solutions of a coupled system for elastic beam equations

In this work, by using fixed point theorem and monotone iterative technique, the author establishes a necessary and sufficient condition of the existence of positive solutions for a class of nonlinear singular elastic beam differential system under reasonable conditions. Moreover, some uniqueness results of positive solution and the estimate of convergent rate of the iterative sequence of solution are obtained.     

The generalized Thomas–Fermi singular boundary value problems for neutral atoms

This paper presents an upper and lower solution theory for singular boundary value problems modelling the Thomas–Fermi equation, subject to a boundary condition corresponding to the neutral atom with Bohr radius equal to its existence interval. Furthermore, we derive sufficient conditions for the existence–construction of the above‐mentioned upper–lower solutions. Copyright © 2005 John Wiley & Sons, Ltd.     

矩阵方程（AX，XB）=（C，D）的反中心对称解及其最佳逼近

本利用矩阵对的广义奇异值分解，得到了(AX，XB)=(C，D)有反中心对称解的充要条件，并给出了其通解的一般表达式，此外，还给出了此矩阵方程的解集合与给定矩阵的最佳逼近的表迭式．     

一类具$p$-Laplace非线性三点边值问题三个正解的存在性

This paper deals with the existence of three positive solutions for a class of nonlinear singular three-point boundary value problem with p-Laplacian. By means of a fixed point theorem duo to Leggett and Williams, sufficient condition for the existence of at least three positive solutions to the nonlinear singular three-point boundary value problem is established     

离散广义系统的平稳振荡

为了研究离散广义系统的平稳振荡，本文利用广义Ｌｙａｐｕｎｏｖ函数方法，给出了一个ｍ周期解存在的充要条件，得出了离散广义系统的周期解的存在性、唯一性、稳定性的有关定理，进而研究具有某种分解的复杂离散广义系统的平稳振荡问题，方法简单易行．     

Saddle-point equilibrium sequence in one class of singular infinite horizon zero-sum linear-quadratic differential games with state delays

ABSTRACT

We consider an infinite horizon zero-sum linear-quadratic differential game with state delays in the dynamics. The cost functional of this game does not contain a control cost of the minimizing player (the minimizer), meaning that the considered game is singular. For this game, definitions of the saddle-point equilibrium and the game value are proposed. These saddle-point equilibrium and game value are obtained by a regularization of the singular game. Namely, we associate this game with a new differential game for the same equation of dynamics. The cost functional in the new game is the sum of the original cost functional and an infinite horizon integral of the square of the minimizer's control with a small positive weight coefficient. This new game is regular, and it is a cheap control game. An asymptotic analysis of this cheap control game is carried out. Using this asymptotic analysis, the existence of the saddle-point equilibrium and the value of the original game is established, and their expressions are derived. Illustrative example is presented.     

ON THE SINGULAR ONE DIMENSIONAL P-LAPLACIAN-LIKE EQUATION WITH NEUMANN BOUNDARY CONDITIONS

1IntroductionInthispaper,weconsiderthesolvabilityofsingularonedimensionalpLaplacian-likeequationwithNeumannboundaryconditionswhereA(()ispositivefor(>0,h(t)EL'([0,1]),gisacontinuousfunctiondefinedon(--co,0)U(0, co)suchthatg(f)-0asf'l-cojg(()- coas(-0 ,g(()---coas(-0--,andg(')(>0for'/0.Afunctionu(t)issaidtobeasolutionof(1.1),ifthefollowingconditionsaresatisfied:Itiseasytoseethatthenecessaryconditionfortheexistenceofthesolutionof(1.1)isInfact,fromtheassumptionsong,weknowthatu(t)/0foralltE(0,1)…     

Nonlinear Separation Approach to Constrained Extremum Problems

In this paper, by virtue of a nonlinear scalarization function, two nonlinear weak separation functions, a nonlinear regular weak separation function, and a nonlinear strong separation function are first introduced, respectively. Then, by the image space analysis, a global saddle-point condition for a nonlinear function is investigated. It is shown that the existence of a saddle point is equivalent to a nonlinear separation of two suitable subsets of the image space. Finally, some necessary and sufficient optimality conditions are obtained for constrained extremum problems.