On the Lipschitzian properties of polyhedral multifunctions

In this paper, we show that for a polyhedral multifunctionF:R ⁿ →R ^m with convex range, the inverse functionF ⁻¹ is locally lower Lipschitzian at every point of the range ofF (equivalently Lipschitzian on the range ofF) if and only if the functionF is open. As a consequence, we show that for a piecewise affine functionf:R ⁿ →R ⁿ ,f is surjective andf ⁻¹ is Lipschitzian if and only iff is coherently oriented. An application, via Robinson's normal map formulation, leads to the following result in the context of affine variational inequalities: the solution mapping (as a function of the data vector) is nonempty-valued and Lipschitzian on the entire space if and only if the solution mapping is single-valued. This extends a recent result of Murthy, Parthasarathy and Sabatini, proved in the setting of linear complementarity problems. Research supported by the National Science Foundation Grant CCR-9307685.     

Minkowski空间中保高斯映射的共形形变

设Ｍｎ为Ｒｉｅｍａｎｎ流形，给定类空浸入：Ｍｎ→Ｒｎ，ｐ，如果存在另一个类空浸入：Ｍｎ→Ｒｎ，ｐ，使与在共形对应之下且对应点的地空间平行，则称类空子流形是可保高斯映射共形形变的．本文给出可保高斯映射共形形变的充要条件．对ｎ＝２，ｐ＝１的情形，如果上述形变是同向的，我们分类了曲面；如果是反向的，我们用主曲率满足的方程来描述．     

各向异性Sobolev空间中拟线性椭圆型方程解的局部有界性

本文在很一般的结构条件下，证明了各向异性Ｓｏｂｏｌｅｖ空间中的拟线性椭圆方程解的局部有界性。     

关于hilbert－ingham不等式和它的应用

本文给出（ｉ）ｈｉｌｂｅｒｔ不等式和ｈｉｌｂｅｒｔ－ｉｎｇｈａｍ不等式一些有意义的共同改进；（ｉｉ）一些ｆｅｊｅｒ－ｒｉｅｓｚ型不等式的改进和（ｉｉｉ）ｈａｒｄｙ不等式的改进．     

Positive Solutionsofp-LaplaceEquation Involving Critical Sobolev Exponent

ＰｏｓｉｔｉｖｅＳｏｌｕｔｉｏｎｓｏｆｐ－ＬａｐｌａｃｅＥｑｕａｔｉｏｎＩｎｖｏｌｖｉｎｇＣｒｉｔｉｃａｌＳｏｂｏｌｅｖＥｘｐｏｎｅｎｔＳｕｎＧｕｏｈｏｎｇ（孙国弘）（ＩｎｓｔｉｔｕｔｅｏｆＭａｔｈｅｍａｔｉｃｓ，ＪｉｌｉｎＵｎｉｖｅｒｓｉｔｙ，Ｃｈ...     

INEXACT DAMPED NEWTON METHOD FOR NONLINEAR COMPLEMENTARITY PROBLEMS

In this paper, we propose an inexact clamped Newton method for solving nonlinear complementarity problems based on the equivalent B-differentiable equations.Global convergence and locally quadratic convergence are obtained,and numerical results are given.     

一类二阶时滞微分方程的振动性判据

本文从不同的角度研究一类二阶时滞微分方程的振动性，得到了一切解振动性的充分条件。改善了文［１］、［２］的工作．     

Completely Positive Definite Maps Over Topological^＊—algebras

ＣｏｍｐｌｅｔｅｌｙＰｏｓｉｔｉｖｅＤｅｆｉｎｉｔｅＭａｐｓＯｖｅｒＴｏｐｏｌｏｇｉｃａｌ－ａｌｇｅｂｒａｓＸｕＴｉａｎｚｈｏｕ（ＤｅｐａｒｔｍｅｎｔｏｆＡｐｐｌｉｅｄＭａｔｈｅｍａｔｉｃｓ，ＢｅｉｊｉｎｇＩｎｓｔｉｔｕｔｅｏｆＴｅｃｈｎｏｆｏｇｙ，...     

Best possibility of the Furuta inequality

Let , and . Furuta (1987) proved that if bounded linear operators on a Hilbert space satisfy , then . In this paper, we prove that the range and is best possible with respect to the Furuta inequality, that is, if or , then there exist which satisfy but .