共查询到19条相似文献,搜索用时 125 毫秒
1.
集值变分不等式问题的例外簇 总被引:3,自引:0,他引:3
本文首先在Banach空间中证明了零调集值映射的一个Leray-Schauder型不动点定理,然后在Hilbert空间中定义了零调集值映射的变分不等式的例外簇,利用本文给出的不动点定理给出了无界集上的变分不等式问题存在解的一个充分条件.此条件弱于许多已知的关于变分不等式问题的解的存在性条件,并由此得到Hilbert空间中几个变分不等式约解的存在性定理. 相似文献
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Fanky极大极小不等式的进一步推广及对变分不等式的应用 总被引:2,自引:0,他引:2
本文引出广义KKM映象的概念,其包含著名的KKM映象为特例.借助于这一映象,我们给出著名的KKM定理和Fan Ky极大极小不等式以一种新的推广形式.作为应用,我们考虑了变分不等式解的存在性问题.本文结果是引文[1~6]中相应结果的改进和发展. 相似文献
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本文中,我们首先给出了一类混合似变分不等式问题.接着,在Banach空间中研究了它的解的存在性和唯一性.最后,讨论了混合似变分不等式问题的扰动问题,并证明了扰动问题的解的存在唯一性定理. 相似文献
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拟变分不等式和社会平衡 总被引:4,自引:4,他引:0
我们在仿紧设置下,在Hausdorff拓扑矢量空间内证明了一个广义拟变分不等式,推广了Zhou-Chen和Aubin的相应结果.作为应用,关于最优化问题的解和亚对策的社会平衡解的两个存在性定理被证明.这些定理改进和推广了Kaczynki-Zeidan和Aubin的最近结果. 相似文献
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给出了变分不等式的例外簇的一个新定义 ,十分简洁地证明它是Zhao ,Han和Qi( 1 999)所定义的例外簇的推广 ,并以此为基础 ,对张、韩和徐 ( 2 0 0 0 )的一般存在性定理给出一个新的证明 . 相似文献
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在Banach空间中引入了一类广义F-互补问题,研究了它与一类变分不等式问题的等价性关系,给出了此类变分不等式问题的解的存在唯一性定理. 相似文献
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本文将单位映射变分不等式和互补问题的解的存在性定理推广到集值映射上.讨论了集值映射互补问题的解与Kakutani不动点之间关系,以及集值映射互补问题的解的计算方法.最后给出了它们在不可微规划中的应用. 相似文献
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Qamrul Hasan Ansari Siegfried Schaible Jen-Chih Yao 《Journal of Global Optimization》2002,22(1-4):3-16
In this paper, we introduce the system of generalized vector equilibrium problems which includes as special cases the system of generalized implicit vector variational inequality problems, the system of generalized vector variational and variational-like inequality problems and the system of vector equilibrium problems. By using a maximal element theorem, we establish existence results for a solution of these systems. As an application, we derive existence results for a solution of a more general Nash equilibrium problem for vector-valued functions. 相似文献
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本文利用局部Lipschitz泛函的临界点理论,来得到一个改进的半线性方程的Landesman Lazer型结果,问题来自于力学,称为变分不等式的特征值问题,在[3]中,D.Goeleven,D.Motreanu和P.D.Panagiotopoulos等人讨论了共振的情形,并得到了弱解的存在性的结果。但是,在他们结论中(见[3]中定理4.1),条件(H1)与(H2)却是互不相容的,本文得到了变分不等式的特征值问题在共振情形下的弱解存在性的相应结果。 相似文献
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In this paper, we consider a new differential variational inequality (DVI, for short) which is composed of an evolution equation and a variational inequality in infinite Banach spaces. This kind of problems may be regarded as a special feedback control problem. Based on the Browder's theorem and the optimal control theory, we show the existence of solutions to the mentioned problem. 相似文献
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This paper introduces a new concept of exceptional family of elements for a finite-dimensional generalized variational inequality
problem. Based on the topological degree theory of set-valued mappings, an alternative theorem is obtained which says that
the generalized variational inequality has either a solution or an exceptional family of elements. As an application, we present
a sufficient condition to ensure the existence of a solution to the variational inequality. The set-valued mapping is assumed
to be upper semicontinuous with nonempty compact convex values. 相似文献
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研究向量集值映射的拟均衡问题的有效解,利用数值化方法与不动点定理,得到解的存在性定理.作为应用,得到广义向量鞍点,向量变分不等式与向量互补问题的存在性定理. 相似文献
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In this paper, we establish the existence of the optimal control for an optimal control problem where the state of the system is defined by a variational inequality problem with monotone type mappings. Moreover, as an application, we get several existence results of an optimal control for the optimal control problem where the system is defined by a quasilinear elliptic variational inequality problem with an obstacle. 相似文献
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In this paper, we first obtain an existence theorem of the solutions for a variational relation problem. An existence theorem
for a variational inclusion problem, a KKM theorem and an extension of the well know Ky Fan inequality will be established,
as particular cases. Some applications concerning a saddle point problem with constraints, existence of a common fixed point
for two mappings and an optimization problem with constraints, will be given in the last section of the paper. 相似文献
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This paper presents the new concept of exceptional family of elements for the variational inequality problem with a continuous function over a general unbounded closed convex set. We establish a characterization theorem that can be used to derive several new existence and compactness conditions on the solution set. Our findings generalize well-known results for various types of variational inequality problems. For a pseudomonotone variational inequality problem, our new existence conditions are both sufficient and necessary. 相似文献
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In this paper, we consider an extension of the notion of well-posedness by perturbations, introduced by Zolezzi for a minimization problem, to a mixed variational inequality problem in a Banach space. We establish some metric characterizations of the well-posedness by perturbations. We also show that under suitable conditions, the well-posedness by perturbations of a mixed variational inequality problem is equivalent to the well-posedness by perturbations of a corresponding inclusion problem and a corresponding fixed point problem. Also, we derive some conditions under which the well-posedness by perturbations of a mixed variational inequality is equivalent to the existence and uniqueness of its solution. 相似文献