Generalized bi-Quasi-Variational Inequalities for Upper Hemi-Continuous Operators in non-Compact Settings

By using the concept of escaping sequences introduced by Border [2], existence theorems on generalized bi-quasi-variational inequalities for F-semi-monotone (re- spectively, bi-quasi-semi-monotone) operators are obtained in non-compact set- tings. As application, an existence theorem on generalized bi-complementarity problem for F-semi-monotone (respectively, bi-quasi-semi-monotone) operator is given in non-compact setting.     

Trace Formulas for Some Singular Differential Operators and Applications

We characterize the convergence of the series ∑ λ^–1_n, where λⁿ are the non‐zero eigenvalues of some boundary value problems for degenerate second order ordinary differential operators and we prove a formula for the above sum when the coefficient of the zero‐order term vanishes. We study these operators both in weighted Hilbert spaces and in spaces of continuous functions. After investigating the boundary behaviour of the eigenfunctions, we give applications to the regularity of the generated semigroups.     

一类减算子的不动点定理及其应用

本文研究了一类具有凹凸性的减算子,给出了这种减算子的不动点的存在性、唯一性和迭代收敛性的一个新的结果,而且在几种方程中得到了应用．     

Some Properties of Quasi-keep-range Operators and Their Applications

ＳｏｍｅＰｒｏｐｅｒｔｉｅｓｏｆＱｕａｓｉ┐ｋｅｅｐ┐ｒａｎｇｅＯｐｅｒａｔｏｒｓａｎｄＴｈｅｉｒＡｐｐｌｉｃａｔｉｏｎｓＬａｉＣｈｕｎｈｕｉ（赖春晖）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＺｈａｎｇｚｈｏｕＴｅａｃｈｅｒｓＣｏｌｅｇｅ，...     

几类增算子方程解的存在唯一性及应用

By using the cone theory and the monotone succession skills,it is studied the existence uniqueness of fixed point for a class of increasing operators without continuity and compactness and concave or convex conditions in Banach spaces.The results presented here improve and generalize some corresponding results for increasing operator.     

一类增算子的不动点定理的推广及应用

利用锥理论单调迭代技巧,研究Banach空间中不具有任何紧性、连续性和凹凸性条件的增算子的不动点的存在唯一性,所得结果改进和推广了增算子的某些已知相应结果.     

Generalized Polar Decompositions for Closed Operators in Hilbert Spaces and Some Applications

We study generalized polar decompositions of densely defined closed linear operators in Hilbert spaces and provide some applications to relatively (form) bounded and relatively (form) compact perturbations of self-adjoint, normal, and m-sectorial operators. Based upon work partially supported by the US National Science Foundation under Grant Nos. DMS-0400639 and FRG-0456306, and the Austrian Science Fund (FWF) under Grant No. Y330.     

几类增算子的不动点定理及其应用

讨论了C[I,E]和L_p[I,E]中几类增算子,得到了若干新的不动点定理,并将其应用于证明非线性微分方程唯一解的存在性.     

Application of Upper Hemi-Continuous Operators on Generalized Bi-quasi-variational Inequalities in Locally Convex Topological Vector Spaces

Let and be Hausdorff topological vector spaces over the field , let be a bilinear functional, and let be a non-empty subset of . Given a set-valued map and two set-valued maps , the generalized bi-quasi-variational inequality (GBQVI) problem is to find a point and a point such that and for all and for all or to find a point a point and a point such that and for all . The generalized bi-quasi-variational inequality was introduced first by Shih and Tan [8] in 1989. In this paper we shall obtain some existence theorems of generalized bi-quasi-variational inequalities as application of upper hemi-continuous operators [4] in locally convex topological vector spaces on compact sets.     

序Banach空间中某些二元算子的不动点及其应用

对于具有上下解的凝聚混合单调算子,在已知文献中仅研究了耦合不动点的存在性.本文研究某些比混合单调算子更广泛的二元算子,得到这类算子不动点的存在性.还通过给定的迭代序列,得到不动点的唯一性或者包含不动点的区间,其推论也是已知结果的改进.最后给出了在椭圆型微分方程求解中的应用.     

八元数中算子之间的关系及应用-Almansi分解

八元数是四元数的非结合推广,由于其乘法的非结合性质,使得其在YangMills方程、黑洞、弦论中具有重要的应用.给出了八元数中算子之间的一些运算关系,并由此导出Almansi分解定理,实现了Almansi分解定理在非交换非结合空间推广的目的.     

几类非线性二元算子方程的迭代解法及其应用

利用锥与半序理论和单调迭代技巧，讨论几类非线性二元算子方程解的存在唯一性，并给出迭代序列收敛速度的估计，改进和推广了某些已有结果．最后给出所得结果的应用。     

Sums of Bisectorial Operators and Applications

We study sums of bisectorial operators on a Banach space X and show that interpolation spaces between X and D(A) (resp. D(B)) are maximal regularity spaces for the problem Ay + By = x in X. This is applied to the study of regularity properties of the evolution equation u′ + Au = f on for or and the evolution equation u′ + Au = f on [0, 2π] with periodic boundary condition u(0) = u(2π) in or      

Banach空间中几类非线性算子方程的迭代解法及其应用

利用单调迭代技巧和锥与半序理论,讨论几类非线性二元算子方程解的存在性与唯一性, 并给出迭代序列收敛速度的估计,改进和推广了某些已有结果.最后给出所得结果的应用.     

On Some Zero-Increasing Operators

We characterize the set of linear operators of the form $$Tx^n = x^n + \sum\limits_{k = 0}^{n - 1} {b_{n,k} x^k ,} n = 0,1, \ldots ,$$ which satisfy Z(T _p ) ≧ Z(p) for every polynomial p, where Z counts the number of zeros on all of R. We also consider the analogous question on [0,∞)].     

Regular Degenerate Separable Differential Operators and Applications

The boundary value problems for differential-operator equations with variable coefficients, degenerated on all boundary are studied. Several conditions for the separability, fredholmness and resolvent estimates in L _p -spaces are given. In applications degenerate Cauchy problem for parabolic equation, boundary value problems for degenerate partial differential equations and systems of degenerate elliptic equations on cylindrical domain are studied.     

Diskcyclicity of Sets of Operators and Applications

In this paper, we introduce and study the diskcyclicity and disk transitivity of a set of operators. We establish a diskcyclicity criterion and give the relationship between this criterion and the diskcyclicity. As applications, we study the diskcyclicty of C₀-semigroups and C-regularized groups. We show that a diskcyclic C₀-semigroup exists on a complex topological vector space X if and only if dim(X)=1 or dim(X)=∞ and we prove that diskcyclicity and disk transitivity of C₀-semigroups (resp C-regularized groups) are equivalent.     

各向异性极大算子及它们的应用

本文证明了一类与异性伸缩相关的极大算子在Ｌ＾ｐ（Ｒ＾ｎ）上是有界的，其中１〈ｐ≤∝，ｎ≥２。进一步，作为应用我们建立了算子Ｔｆ（ｘ）＝ｓｕｐε〉０│Ｔεｆ（ｘ）│Ｌ＾ｐ有界性，其中Ｔε是带有变化核的奇异积分。