非紧集上不连续函数的Ky Fan不等式及其等价形式和应用

证明了非紧集上不具有任何连续性的函数弱Ky Fan点的存在性,给出了在函数只具非常弱的连续性和凸性条件下非紧集上Ky Fan不等式解的存在性,并给出它的两种等价形式.作为应用:(1)得到Ky Fan截口定理和Fan-Browder不动点定理的推广;(2)应用于博弈理论,得到几个新的Nash平衡存在性定理.     

Generalized variational-like inequalities for pseudo-monotone type III operators

Our aim in this paper is mainly to prove some existence results for solutions of generalized variational-like inequalities with (η,h)-pseudo-monotone type III operators defined on non-compact sets in topological vector spaces.     

拓扑空间上的KKM定理,不动点定理,广义变分不等式

引进没有任何凸结构的拓扑空间上的广义R-KKM映射的定义并利用古典的KKM原理得到一般拓扑空间上的KKM型定理以及若干个变形结果,然后作为应用给出了非紧的拓扑空间上不动点定理和广义变分不等式解的存在性定理.     

关于广义变分不等式与广义拟变分不等式

本文在非常一般的框架下,建立了极大极小不等式,广义变分不等式和广义拟变分不等式,证明了解的存在定理,且它们是在非紧集上得到的,从而推广和改进了[3～13]中的相应结果.     

On generalized operator quasi-equilibrium problems

In this paper, we will introduce the generalized operator equilibrium problem and generalized operator quasi-equilibrium problem which generalize the operator equilibrium problem due to Kazmi and Raouf [K.R. Kazmi, A. Raouf, A class of operator equilibrium problems, J. Math. Anal. Appl. 308 (2005) 554-564] into multi-valued and quasi-equilibrium problems. Using a Fan-Browder type fixed point theorem in [S. Park, Foundations of the KKM theory via coincidences of composites of upper semicontinuous maps, J. Korean Math. Soc. 31 (1994) 493-519] and an existence theorem of equilibrium for 1-person game in [X.-P. Ding, W.K. Kim, K.-K. Tan, Equilibria of non-compact generalized games with L^∗-majorized preferences, J. Math. Anal. Appl. 164 (1992) 508-517] as basic tools, we prove new existence theorems on generalized operator equilibrium problem and generalized operator quasi-equilibrium problem which includes operator equilibrium problems.     

拓扑空间上不动点和具有上下界的变分不等式

ωω根据广义凸空间上的KKM型定理和Fan-Browder型不动点定理, 得到了没有凸和线性结构且没有紧致框架的拓扑空间上的Φ -映射和弱Φ -映射的若干个新的不动点定理. 作为应用, 在非紧致的拓扑空间上讨论了具有上下界的变分不等式解的存在性问题.     

A new class of random completely generalized strongly nonlinear quasi-complementarity problems for random fuzzy mappings

In this paper, we introduce and study a new class of random completely generalized strongly nonlinear quasi - complementarity problems with non-compact valued random fuzzy mappings and construct some new iterative algorithms for this kind of random fuzzy quasi-complementarity problems. We also prove the existence of random solutions for this class of random fuzzy quasicomplementarity problems and the convergence of random iterative sequences generated by the algorithms.     

Semilinear subelliptic problems without compactness on Lie groups

An abstract version of concentration compactness on Hilbert spaces applies to to actions of non-compact Lie groups. Using the concentration compactness argument we prove existence of solutions for semilinear problems involving sub-Laplacians on the whole Lie group and on their cer-tain non-compact subsets, including minimizers for Sobolev inequalities. The result is stated for any real connected finite-dimensional Lie group.     

A class of Kazdan-Warner typed equations on non-compact Riemannian manifolds

In this paper,we discuss a Kazdan-Warner typed equation on certain non-compact Rie- mannian manifolds.As an application,we prove an existence theorem of Hermitian-Yang-Mills-Higgs metrics on holomorphic line bundles over certain non-compact K(?)hler manifolds.     

Isometry Groups and Geodesic Foliations of Lorentz Manifolds. Part I: Foundations of Lorentz Dynamics

This is the first part of a series on non-compact groups acting isometrically on compact Lorentz manifolds. This subject was recently investigated by many authors. In the present part we investigate the dynamics of affine, and especially Lorentz transformations. In particular we show how this is related to geodesic foliations. The existence of geodesic foliations was (very succinctly) mentioned for the first time by D'Ambra and Gromov, who suggested that this may help in the classification of compact Lorentz manifolds with non-compact isometry groups. In the Part II of the series, a partial classification of compact Lorentz manifolds with non-compact isometry group will be achieved with the aid of geometrical tools along with the dynamical ones presented here. Submitted: October 1997, revised: November 1998.     

Functional inequality on path space over a non-compact Riemannian manifold

We prove the existence of the O-U Dirichlet form and the damped O-U Dirichlet form on path space over a general non-compact Riemannian manifold which is complete and stochastically complete. We show a weighted log-Sobolev inequality for the O-U Dirichlet form and the (standard) log-Sobolev inequality for the damped O-U Dirichlet form. In particular, the Poincaré inequality (and the super Poincaré inequality) can be established for the O-U Dirichlet form on path space over a class of Riemannian manifolds with unbounded Ricci curvatures. Moreover, we construct a large class of quasi-regular local Dirichlet forms with unbounded random diffusion coefficients on path space over a general non-compact manifold.     

集值映射的Nash平衡点的存在定理

本文引入了集值映射的Nash平衡点的概念，它以通常的Nash平衡点及Loose Nash平衡点为特例，并在紧和非紧的假设下，得到集值映射的Nash平衡点的存在定理，其中在非紧的情况下使用escaping序列的定义．     

Equilibrium problems and variational inequalities in topological vector spaces

An existence result for the equilibrium problem is proved in a general topological vector space. As applications, existence results are derived for variational inequality problems, vector equilibrium problems and vector variational inequality problems. Our results extend and unify a number of existence theorems in non-compact cases     

Existence of solution of the logarithmic diffusion equation with bounded above Gauss curvature

We give a simple proof of an extension of the existence results of Ricci flow of Giesen and Topping (2010, 2011) [15], [20], on incomplete surfaces with bounded above Gauss curvature without using the difficult Shi’s existence theorem of Ricci flow on complete non-compact surfaces and the pseudolocality theorem of Perelman [7] on Ricci flow. We will also give a simple proof of a special case of the existence theorem of Topping (2010) [16] without using the existence theorem of Shi (1989) [9].     

一类非线性奇异边值问题的正解

运用正则锥上的非紧增算子的不动点的存在性,讨论了一般非线性Strum-Liouville奇异边值问题,得出了有关解的存在性的条件及其等价条件.     

Semistable Twisted Holomorphic Chains on Non-Compact Kähler Manifolds

In this paper, the author proves a generalized Donaldson-Uhlenbeck-Yau theorem for twisted holomorphic chain on a non-compact K\"ahler manifold. As an application, the author obtains a Bogomolov type Chern numbers inequality for semistable twisted holomorphic chain.     

A generalized KKMF principle

We present in this paper a generalized version of the celebrated Knaster-Kuratowski-Mazurkiewicz-Fan's principle on the intersection of a family of closed sets subject to a classical geometric condition and a weakened compactness condition. The fixed point formulation of this generalized principle extends the Browder-Fan fixed point theorem to set-valued maps of non-compact convex subsets of topological vector spaces.     

Existence of solutions for the p-Laplacian with critical Sobolev exponent and convection

In this article, we study the existence of solutions for the p-Laplacian involving critical Sobolev exponent and convection based on the theory of the Leray–Schauder degree for non-compact mappings.     

A new generalization of the Yannelis–Prabhakar equilibrium existence theorem for abstract economies

In this paper, we prove an intersection theorem for an infinite family of correspondences defined on non-compact spaces, and apply this result to give a new generalization of the Yannelis–Prabhakar existence theorem for equilibrium of abstract economies.     

Beispiele von Pseudo-Differentialoperator-Algebrenfl

Discussion of methods in theory of Partial Differential Operators (and Pseudo-Differential Operators) which are based on Gel'fand theory of commutative Banach Algebras. These methods all are discussed for the (non-compact) manifold Rⁿ, for L^p/-SobolefF spaces W_p,k (including k = ∞) and for operators of "Laplace-type", which, crudely, amounts to "elliptic type". Generalizations to general non-compact manifolds and to hypo-elliptic operators have been worked out in detail in [6], for example. Two types of symbol are introduced for a (Pseudo)-differential operator: the Laplace-symbol-quotient ^s (of order s) and the symbol σ. Among the results we have (a) necessary and sufficient criteria for the existence of an W^:p,-Fredholm inverse, (b) essential self-adjointness and (c) characterization of the essential spectrum of elliptic (Pseudo-) Differential operators.