2007年高考中解析几何存在性问题浅析

涉及到某种数学对象是否存在的问题，常称为存在性问题，存在性问题根据其问题特征大体可以分为如下三类：1）证明某种对象一定存在，可以称为“肯定型问题”；2）证明某种对象一定不存在，可以称为“否定型问题”；3）探究某种对象是否存在，或者探究某类对象存在的条件，可以称为“探究型存在性问题”。     

半导体漂移 扩散方程稳态解的存在性

考虑半导体方程稳态模型的混合边值问题，应用Schauder不动点定理证明了逼近解的存在性，通过一系列先验估计的获得，利用紧致性原理证明了稳态解的存在性.     

具有一个高阶奇点和两个零特征根的一类多项式系统

本文讨论了具有一个高阶奇点和两个零特征根的一类２ｎ＋１次系统，证明了这类系统可以存在两个ｎ阶细焦点，给出极限存在性和不存在性的条件，并证明了无穷远分界线环的存在性。     

非线性微分方程零解的全局吸引性与包围高阶奇点的极限环的存在性

非线性微分方程零解的全局吸引性与包围高阶奇点的极限环的存在性王向荣，冯滨鲁，韩茂安（山东矿业学院数学系泰安２７１０１９）关键词：全局吸引性；极限环；存在性ＡＭＳ（１９９１）主题分类：３４Ｃ０５．考虑系统假设ｈ，Ｆ，ｇ均连续且满足解的存在唯一性条件，且...     

一类非线性大系统的周期解

本文讨论了一类非线性大系统周期解的存在性． 利用指数型二分性和不动点方法，建立了保证周期解存在性的条件，所得结果推广了文［１］的主要结果．     

半导体漂移-扩散方程速度饱和情形的稳态解

考虑半导体方程稳态模型的混合边值问题，应用Schauder不动点定理证明了逼近解的存在性，通过一系列先验估计的获得，利用紧致性原理证明了稳态解的存在性。     

带雪崩项半导体方程稳态解的存在性

考虑带雪崩项半导体方程稳态模型的混合边值问题，应用Schauder不动点定理证明了逼近解的存在性，通过一系列先验估计的获得，利用紧致性原理证明了稳态弱解的存在性．     

纯交换系统均衡存在性与拓朴学

本文对纯交换经济系统中均衡的存在性，介绍了一种应用拓扑学的证明方法，它包含了对更一般均衡模型存在性论证的基本特色。     

随机环境中耦合空间的不变测度存在性

本文研究了随机环境中耦合空间上不变测度存在性问题，证明了一些存在性定理．     

不动点在讨论驻点存在性问题中的应用

本文通过建立不动点与驻点之间的关系，从而利用不动点的存在性来确定函数驻点的存在性。     

Almost Periodic Solutions of Nonlinear Second Order Differential Equations

We provide existence results for almost periodic solutions of nonlinear second order ordinary differential equations. The results extend existence results for periodic solutions of periodic equations, where the existence of periodic sub and supersolutions implied the existence of periodic solutions.     

System of Generalized Vector Quasi-Equilibrium Problems with Applications to Fixed Point Theorems for a Family of Nonexpansive Multivalued Mappings

In this paper, we establish the existence theorems of the generalized vector quasi-equilibrium problems. From some existence theorem, we establish fixed point theorems for a family of lower semicontinuous or nonexpansive multivalued mappings. We also obtain the existence theorems of system of mixed generalized vector variational-like inequalities and existence theorems of the Debreu vector equilibrium problems and the Nash vector equilibrium problems.     

一类泛函微分方程半正问题的正周期解

运用Krasnosel’skii不动点理论研究了一类含参泛函微分方程半正问题正周期解的存在性．获得了当参数充分小时正周期解的存在性结果以及半正问题正周期解存在的充分条件．丰富了一阶泛函微分方程解的存在性理论．     

Variational inclusions problems with applications to Ekeland’s variational principle,fixed point and optimization problems

In this paper, we prove the existence theorems of two types of systems of variational inclusions problem. From these existence results, we establish Ekeland’s variational principle on topological vector space, existence theorems of common fixed point, existence theorems for the semi-infinite problems, mathematical programs with fixed points and equilibrium constraints, and vector mathematical programs with variational inclusions constraints.     

Square of countably compact groups without non-trivial convergent sequences

We show in ZFC that the existence of a countably compact Abelian group without non-trivial convergent sequences implies the existence of a countably compact group whose square is not countably compact.This improves a result obtained by van Douwen in 1980: the existence of a countably compact Boolean group without non-trivial convergent sequences implies the existence of two countably compact groups whose product is not countably compact in ZFC.Hart and van Mill showed in 1991 the existence of a countably compact group whose square is not countably compact under Martin's Axiom for countable posets. We show that the existence of such an example does not depend on some form of Martin's Axiom.     

Traveling waves in delayed lattice dynamical systems with competition interactions

This paper deals with the existence of traveling wave solutions of a class of delayed system of lattice differential equations, which formulates the invasion process when two competitive species are invaders. Employing the comparison principle of competitive systems, a new cross-iteration scheme is given to establish the existence of traveling wave solutions. More precisely, by the cross-iteration, the existence of traveling wave solutions is reduced to the existence of an admissible pair of upper and lower solutions. To illustrate our main results, we prove the existence of traveling wave solutions in two delayed two-species competition systems with spatial discretization. Our results imply that the delay appeared in the interspecific competition terms do not affect the existence of traveling wave solutions.     

线性增长条件下一类非线性梁方程解的存在性

考察了一类非线性四阶两点边值问题的解的存在性.通过构造适当的Banach空间并且利用积分方程建立了一个存在定理.主要工具是Leray-Schauder非线性抉择.本文表明,如果非线性项在其定义域的某个有界子集上的增长速度是线性的,该问题可能存在解.     

Existence of solutions of non-autonomous second order functional differential equations with infinite delay

In this paper the existence of solutions of a non-autonomous abstract retarded functional differential equation of second order with infinite delay is considered. Assuming the existence of an evolution operator corresponding to the associate abstract Cauchy problem of second order, we establish the existence of mild solutions of the functional equation. Furthermore, we study the existence of classical solutions of the abstract Cauchy problem of second order and we apply these results to establish the existence of classical solutions of the functional equation. Finally, we apply our results to study the existence of solutions of the non-autonomous wave equation with delay.     

Existence of equilibria for generalized games without paracompactness

In this paper, we first prove an existence theorem of maximal elements without any paracompactness. Then, we establish an existence theorem of equilibrium points of generalized games with infinite many players and without any paracompactness, by applying our maximal element existence theorem. Our equilibrium existence theorem answers the two questions raised by Kim [6] in the affirmative.     

An Elementary Approach to the Daniell-Kolmogorov Theorem and Some Related Results

We give a short elementary proof of the Daniell-Kolmogorov existence theorem for probability measures on product spaces, assuming nothing but the existence of Lebesgue measure on the unit interval. Related approaches are used to prove the existence of regular conditional distributions directly on Polish spaces, and to establish the existence of random measures and sets with given finite-dimensional distributions or hitting probabilities, respectively.