群体多目标最优化的Lagrange对偶性

本文建立了目标和约束为不对称的群体多目标最优化问题的Lagrange对偶规划，在问题的联合弱有效解意义下，得到群体多目标最优化Lagrange型的弱对偶定理、基本对偶定理、直接对偶定理和逆对偶定理。     

YoshiZawa型周期解定理和Massera型周期解定理研究进展简介

微分方程解的有界性和周期解的存在性是檄分方程理论研究中的两个重要课题，二者之间有着紧密的联系．在解的有界性与周期解的存在性的研究中，Yoshizawa周期解定理和Massera周期解定理是非常重要的结果，具有重要的理论意义和应用价值．本文以Yoshizawa型周期解定理和Massera型周期解定理的研究为主，简要介绍泛函微分方程周期解理论研究方面的一些新进展。     

一个Mini Max定理和一类二阶Hamiltont系统的解的唯一性5

推广了Stepan A．Tersian的关于g（u）=2^-1（Au，u）-Ф（u）型泛函的一个Mini Max定理．利用这一推广了的MiniMax定理，研究了一类受迫振动下二阶Hamilton系统的边界值问题的解，获得了这类二阶Hamilton系统边界值问题的解的一个唯一性定理．     

解斜三角形

本单元的重点是：正弦定理、余弦定理，求周长、面积，判断三角形的形状，与解斜三角形有关的实际应用问题．综合运用正弦定理、余弦定理和内角和定理等基础知识解决几何问题和实际问题，有助于培养和提高学生分析问题和解决问题的能力．     

一类中值定理双介值问题命题的注记

在中值定理类双介值问题的命题中,很多命题者没有注意到结论的平凡性.文章借助于微分Darboux定理,证明了对应的非平凡问题解的存在性.     

集值映射向量优化问题的e-真有效解

引入了集值映射向量优化问题的αe-弱有效解、e-真有效解、e-真鞍点概念,在近似广义C-次似凸条件下,建立了e-真有效解的标量化定理、Lagrang乘子定理和e-真鞍点定理,并讨论了集值映射向量优化问题的αe-弱有效解的标量化定理和Laugrange乘子定理,推广了已有结果。     

一类带参数的半线性椭圆方程正径向解的存在性研究

主要讨论一类带参数的半线性椭圆型方程在一定的边值条件下的解的存在性问题.主要利用上下解方法和不动点定理解决方程解的存在性问题,重点讨论了解存在的充分条件,并以定理的形式给出具体的证明.     

一类非线性中立型时滞微分方程周期解的存在性

本文利用抽象连续定理，研究了一类非线性时滞微分方程x′(t)=f(t，x(t)，x(t-τ)，x′(t-τ)) p(t)的周期解问题，并在滞量τ的不同范围内分别得到了周期解存在的充要条件。     

超双曲型方程定性研究的一些问题

本文是超双曲型方程定性研究的一个综合报导，它包括L.Asgeirsson中量定理的一个新证法；中量定理的推广；广义势解的非解析性；解的拓展性，境界值问题；基本解问题。     

达布定理和比较定理思想在中值定理类问题中的运用

微分达布定理表明区间内的导函数具有介值性,这使得我们在考虑一些数学分析问题时,往往可以不需要最高阶导函数的连续性.而在微分方程理论中,比较定理的思想对于解的估计非常重要.本文利用比较定理的思想将中值定理类问题转化为微分方程解的估计问题,对于在数学分析的学习中提高学生的认识和兴趣很有意义.     

On random variational inclusions with random fuzzy mappings and random relaxed cocoercive mappings

In this paper, we introduce and study the random variational inclusions with random fuzzy and random relaxed cocoercive mappings. We define an iterative algorithm for finding the approximate solutions of this class of variational inclusions and establish the convergence of iterative sequences generated by proposed algorithm. Our results improve and generalize many known corresponding results.     

含H-单调映象的完全广义非线性变分包含

引入和研究了一类新的完全广义非线性变分包含.在Hilbert空间中利用与H-单调映象相联系的预解算子的性质,对完全广义非线性变分包含建立了解的存在性定理和构造了一种新的迭代算法,证明了由此算法生成的迭代序列强收敛于精确解.其算法和结果是最近文献中相应算法和结果的改进和推广.     

Completely generalized nonlinear variational inclusions for fuzzy mappings

In this paper, we introduce and study a new class of completely generalized nonlinear variational inclusions for fuzzy mappings and construct some new iterative algorithms. We prove the existence of solutions for this kind of completely generalized nonlinear variational inclusions and the convergence of iterative sequences generated by the algorithms.     

关于fuzzy映射的完全广义混合强非线性变分包含

引入并研究了Hilbert空间中一类新的关于fuzzy映射的完全广义混合强非线性变分包含，利用极大单调映射的预解算子技巧构造迭代算法．并证明此变分包含的解的存在性及由迭代算法所生成的迭代序列的收敛性。所得结果改进并推广以往所得的相应结果。     

A new class of generalized nonlinear implicit quasivariational inclusions with fuzzy mappings

In this paper, we introduce and study a new class of generalized nonlinear implicit quasivariational inclusions with fuzzy mappings. An existence theorem of solutions is proved without compactness assumptions. A new iterative algorithm is suggested and analysed. The convergence of iterative sequences generated by the new algorithm are also given. As special cases, some known results are also discussed.     

On a new system of nonlinear A-monotone multivalued variational inclusions

In this paper, we introduce and study a new system of nonlinear A-monotone multivalued variational inclusions in Hilbert spaces. By using the concept and properties of A-monotone mappings, and the resolvent operator technique associated with A-monotone mappings due to Verma, we construct a new iterative algorithm for solving this system of nonlinear multivalued variational inclusions associated with A-monotone mappings in Hilbert spaces. We also prove the existence of solutions for the nonlinear multivalued variational inclusions and the convergence of iterative sequences generated by the algorithm. Our results improve and generalize many known corresponding results.     

模糊映射的完全广义混合型强变分不等式

研究关于模糊映射的一类新的变分不等式－模糊映射的完全广义混合型强变分不等式,得到此类变分不等式解的存在定理分解的一个逼近算法,推广了文[4]和文[8]的主要结果。     

一类广义变分包含的迭代解

介绍一类新的涉及集值映射的变分包含问题，构造其迭代序列，并证明迭代序列收敛于变分包含问题的解，给出迭代序列与解的误差估计。     

A new method for a class of nonlinear variational inequalities with fuzzy mappings

In this paper, we construct a new iterative algorithm of solution for a new class of nonlinear variational inequalities with fuzzy mappings and give some convergence analysis of iterative sequences generated by algorithm.     

A novel proof of the existence of solutions for a new system of generalized mixed quasi-variational-like inclusions involving (<Emphasis Type="Italic">A</Emphasis>, <Emphasis Type="Italic">η</Emphasis>, <Emphasis Type="Italic">m</Emphasis>)-accretive operators

In this paper, we introduce a new system of generalized mixed quasi-variational-like inclusions with (A, η, m)-accretive operators and relaxed cocoercive mappings. By using the fixed point theorem of Nadler, we prove the existence of solutions for this general system of generalized mixed quasi-variational-like inclusions and its special cases. The results in this paper unify, extend and improve some known results in the literature. The novel proof method is simpler than those iterative algorithm approach for proving the existence of solutions of all classes of system of set-valued variational inclusions in the literature.