关于Yamabe问题

本文讨论了Yamabe方程的摄动方程解的收敛性质,由此给出Aubin的结果一个新证明,证明不需要用带最好常数的Sobolev不等式.并且给出了一个未被Aubin结果所包括的存在定理。最有趣的是,文中所获得的解一般是非极小的。     

欧氏空间中完备极小子流形

在一个类似于稳定不等式的条件下,得到了欧氏空间中完备极小子流形的Bernstein型定理.我们的结果部分推广了Li H.Z.和Wei G.X.的定理.     

对Aubin与Frankowska关于闭凸集值映射最小选择的一个结果的讨论

本文对J.-P.Aubin与H.Frankowska最近关于自反严格凸Banach空间中闭凸集值映射最小选择连续的一个结果加以讨论,首先在比自反性较强的一类空间中讨论了在弱于J.-P.Aubin与H.Frankowska的条件下闭凸集值映射最小选择的连续性,其次对J.-P.Aubin与H.Frankowska的结果给出一个新的简单证明,最后用反例说明本文给出的条件与J.-P.Aubin与H.Frankowska条件都是充分而不必要的.     

FC-空间中的参数型KKM定理及其应用

首先在Fc-空间中证明了一个特征性质,然后通过引进线性序空间,利用集合的连通性,在非紧的FC-空间中证明了一个参数型KKM定理.应用参数型KKM定理得到非紧的极大极小不等式、鞍点定理和截口定理.这些结果改进和推广了这个领域中的一些相关结果.     

平均反射随机微分方程的传输不等式[英文]

本文研究平均反射随机微分方程的传输不等式的问题. 利用Girsanov定理和鞅表示定理, 针对该方程在连续轨道空间上, 关于一致收敛范数, 获得Talagrand传输不等式. 这推广了吴黎明和张正良(2004)得到的结果.     

FC-空间中的Ky Fan匹配定理及其对极大极小不等式的应用

建立了FC-空间中弱转移紧开覆盖的匹配定理.作为应用,获得了FC-空间中的重合定理、不动点定理、极大元定理和极大极小不等式.我们的结论统一、改进和推广了一些近期文献的已知结果.     

二阶非线性阻尼微分不等式解的振动性质

研究了一类二阶非线性阻尼微分不等式解的振动性质.在一定条件下,建立了两个新的振动性定理,推广和改进了已知的结果.     

二阶非线性摄动微分不等式的振动性质

研究了一类二阶非线性摄动微分不等式解的振动性质.在一定条件下,应用分类讨论和分析的方法,建立了两个新的振动性定理,推广和改进了已知的结果.     

Aleksandrov-Fenchel不等式及应用

本文运用Aleksandrov-Fenchel不等式,首先推广了Lutwak,Bonnesen和Fenchel等建立的三个有用的定理,这三个定理在解决某些唯一性问题中扮演着重要角色.然后,把这些结果从一般的混合体积和投影体推广到混合投影体的极和混合仿射表面积上,获得了一些较理想的结果.     

FC-度量空间中新的不动点定理及其对鞍点的应用

利用KKM技巧,建立了FC-度量空间中转移紧开值映射的新的不动点定理.作为应用,获得了FC-度量空间中的极大元定理、相交定理、极大极小不等式和鞍点定理.我们的结论统一、改进和推广了一些近期文献的已知结果.     

Aubin property and uniqueness of solutions in cone constrained optimization

We discuss conditions for the Aubin property of solutions to perturbed cone constrained programs, by using and refining results given in Klatte and Kummer (Nonsmooth equations in optimization. Kluwer, Dordrecht, 2002). In particular, we show that constraint nondegeneracy and hence uniqueness of the multiplier is necessary for the Aubin property of the critical point map. Moreover, we give conditions under which the critical point map has the Aubin property if and only if it is locally single-valued and Lipschitz.     

非自治系统的生存定理

在某些适当的条件下证明了广义生存定理，并且给出一个例子说明Aubin提出的生存定理的假设条件一般讲是不能改进的。     

Aubin cores and bargaining sets for convex cooperative fuzzy games

In this paper, we deal with Aubin cores and bargaining sets in convex cooperative fuzzy games. We first give a simple and direct proof to the well-known result (proved by Branzei et al. (Fuzzy Sets Syst 139:267–281, 2003)) that for a convex cooperative fuzzy game v, its Aubin core C(v) coincides with its crisp core C ^cr (v). We then introduce the concept of bargaining sets for cooperative fuzzy games and prove that for a continuous convex cooperative fuzzy game v, its bargaining set coincides with its Aubin core, which extends a well-known result by Maschler et al. for classical cooperative games to cooperative fuzzy games. We also show that some results proved by Shapley (Int J Game Theory 1:11–26, 1971) for classical decomposable convex cooperative games can be extended to convex cooperative fuzzy games.     

On implicit function theorems for set-valued maps and their application to mathematical programming under inclusion constraints

In this paper we establish some implicit function theorems for a class of locally Lipschitz set-valued maps and then apply them to investigate some questions concerning the stability of optimization problems with inclusion constraints. In consequence we have an extension of some of the corresponding results of Robinson, Aubin, and others.     

On Quantitative Stability in Optimization and Optimal Control

We study two continuity concepts for set-valued maps that play central roles in quantitative stability analysis of optimization problems: Aubin continuity and Lipschitzian localization. We show that various inverse function theorems involving these concepts can be deduced from a single general result on existence of solutions to an inclusion in metric spaces. As applications, we analyze the stability with respect to canonical perturbations of a mathematical program in a Hilbert space and an optimal control problem with inequality control constraints. For stationary points of these problems, Aubin continuity and Lipschitzian localization coincide; moreover, both properties are equivalent to surjectivity of the map of the gradients of the active constraints combined with a strong second-order sufficient optimality condition.     

Quantitative Stability of a Generalized Equation

The paper is devoted to the study of several stability properties (such as Aubin/Lipschitz-like property, calmness and isolated calmness) of a special non-monotone generalized equation. The theoretical results are applied in the theory of non-regular electrical circuits involving electronic devices like ideal diode, practical diode, and diode alternating current.     

Banach空间中线性算子的集值度量右逆的表示及应用

在自反 Ｂａｎａｃｈ空间中运用对偶映射方法给出闭稠定满射线性算子的集值度量右逆的表示．拓广了已有的相应结果．     

抛物型发展微分包含的解与解集的性质

在Ｂａｎａｃｈ空间中研究与时间有关的抛物型发展微分包含,这一问题与非线性分布参数控制系统的研究密切相关·我们证明了ｍｉｌｄ＿解的存在性,同时研究了解集的拓扑性质·本文的研究发展和推广Ｊ．Ｐ．Ａｕｂｉｎ等人的方向和结果·     

Hessian Comparison and Spectrum Lower Bound of Almost Hermitian Manifolds

The authors obtain a complex Hessian comparison for almost Hermitian manifolds, which generalizes the Laplacian comparison for almost Hermitian manifolds by Tossati, and a sharp spectrum lower bound for compact quasi Kähler manifolds and a sharp complex Hessian comparison on nearly Kähler manifolds that generalize previous results of Aubin, Li Wang and Tam-Yu.     

Book review

Applied Functional Analysis, by Jean-Pierre Aubin, Wiley-Intersciece 1979. Reviewed by Roy B. Leipnik