批量到达的、具有两种服务阶段和服务中断的重试排队系统的适定性

运用Hille-Yosida定理,Phillips定理与Fattorini定理证明批量到达、具有两种服务阶段和服务中断的重试排队系统存在唯一的、非负的、满足概率性质的时间依赖解.     

Noncommutative Riesz theorem and weak Burnside type theorem on twisted conjugacy

The paper consists of two parts. In the first part, we prove a noncommutative analog of the Riesz(— Markov—Kakutani) theorem on representation of functionals on an algebra of continuous functions by regular measures on the underlying space. In the second part, using this result, we prove a weak version of a Burnside type theorem on twisted conjugacy for arbitrary discrete groups.     

Modifications of the Ricci tensor and applications

By using two modified Ricci tensors, we prove some theorems which correspond to Myers’s diameter estimate theorem and Bochner’s vanishing theorem.     

Some applications of Cartan's theorem to normality and semiduality of gap power series

In this paper we give partial solutions to some questions concerning analytic functions with AP-Gaps raised by Pinto, Ruscheweyh and Salinas (cf. [9], [12]) using a theorem of H. Cartan which extends Montel's theorem on analytic functions omitting the values 0 and 1. Using the same method, we also prove a generalization of a theorem in [9] on the dual hull of sets containing two elements.     

The split common null point problem for generalized resolvents in two banach spaces

In this paper, we consider the split common null point problem in two Banach spaces. Then, using the generalized resolvents of maximal monotone operators and the generalized projections, we prove a strong convergence theorem for finding a solution of the split common null point problem in two Banach spaces. It seems that such a theorem for generalized resolvents is the first of its kind outside Hilbert spaces.     

Existence and multiplicity of solutions for second order periodic systems with the p-Laplacian and a nonsmooth potential

In this paper we study nonlinear periodic systems driven by the ordinary p-Laplacian with a nonsmooth potential. We prove an existence theorem using a nonsmooth variant of the reduction method. We also prove two multiplicity results. The first is for scalar problems and uses the nonsmooth second deformation lemma. The second is for systems and it is based on the nonsmooth local linking theorem.     

Existence and multiplicity of solutions for second order periodic systems with the <Emphasis Type="Italic">p</Emphasis>-Laplacian and a nonsmooth potential

In this paper we study nonlinear periodic systems driven by the ordinary p-Laplacian with a nonsmooth potential. We prove an existence theorem using a nonsmooth variant of the reduction method. We also prove two multiplicity results. The first is for scalar problems and uses the nonsmooth second deformation lemma. The second is for systems and it is based on the nonsmooth local linking theorem.     

An existence theorem for a generalized self-dual Chern–Simons equation and its application

In this paper, we establish an existence theorem for a generalized self-dual Chern–Simons equation over a doubly periodic domain and use the existence theorem to prove the existence of doubly periodic self-dual vortices in a Maxwell–Chern–Simons model with non-minimal coupling. We find a necessary and sufficient condition for the existence of solutions of the generalized Chern–Simons equation. We prove the existence result by using two methods, a super- and sub-solution method and a constrained minimization method. Our main contribution is that we find a general inequality-type constraint by using the second method and it maybe applied to some related problems with the similar structures.     

L0-线性函数的Hahn-Banach扩张定理的几何形式与随机赋范模中的Goldstine-Weston定理

本文给出了关于L⁰- 线性函数的Hahn-Banach 扩张定理的几何形式并证明这个几何形式等价于它的代数形式. 进一步, 我们利用这个几何形式给出了随机局部凸模中熟知的基本分离定理的一个新的且简单的证明. 最后, 利用这个分离定理, 我们同时在两种拓扑 —(ε, λ)- 拓扑和局部L⁰- 凸拓扑下证明了随机赋范模中的Goldstine-Weston 稠密性定理, 并举出一个反例说明在局部L⁰- 凸拓扑下如果随机赋范模不具有可数连接性质, 则Goldstine-Weston 稠密性定理不一定成立.     

Local existence of the solution to the initial‐boundary value problem in nonlinear thermomicroelasticity theory

We prove a theorem about local existence (in time) of the solution to the first initial‐boundary value problem for a nonlinear system of equation of the thermomicroelasticity theory. At first, we prove existence, uniqueness and regularity of the solution to this problem for the associated linearized system by using the method of semi‐group theory. Next, basing on this theorem, we prove an energy estimate for the solution to the linearized system by applying the method of Sobolev space. At the end, using the Banach fixed point theorem, we prove that the solution of our nonlinear problem exists and is unique. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

具有变号非线性项的二阶三点边值问题的两个正解

本文首先证明双锥上的一个不动点定理，并通过该定理研究一类具有变号非线性项的二阶三点边值问题两个正解的存在性．同时，该三点边值问题相关的Green函数也被给出．     

齐次群上二阶半线性偏微分方程的一类Picone型恒等式和Sturmian比较定理

本文给出了齐次群上的一类广义Picone型恒等式,由此证明了以下半线性方程组(其中 表示齐次群上的广义梯度)的Sturmian比较定理及一类振荡定理,并用于Heisenberg群上一类半线性方程.然后利用这里的广义Picone型恒等式证明了Heisenberg群上一类更一般的Hardv型不等式     

Krein–Langer Factorization and Related Topics in the Slice Hyperholomorphic Setting

We study various aspects of Schur analysis in the slice hyperholomorphic setting. We present two sets of results: first, we give new results on the functional calculus for slice hyperholomorphic functions. In particular, we introduce and study some properties of the Riesz projectors. Then we prove a Beurling–Lax type theorem, the so-called structure theorem. A crucial fact which allows to prove our results is the fact that the right spectrum of a quaternionic linear operator and the point S-spectrum coincide. Finally, we study the Krein–Langer factorization for slice hyperholomorphic generalized Schur functions. Both the Beurling–Lax type theorem and the Krein–Langer factorization are far-reaching results which have not been proved in the quaternionic setting using notions of hyperholomorphy other than slice hyperholomorphy.     

FIXED POINT THEOREMS FOR MEIR-KEELER CONDENSING OPERATORS VIA MEASURE OF NONCOMPACTNESS

In this article,we introduce the notion of Meir-Keleer condensing operator in a Banach space,a characterization using L-functions and provide a few generalization of Darbo fixed point theorem.Also,we introduce the concept of a bivariate Meir-Keleer condensing operator and prove some coupled fixed point theorems.As an application,we prove the existence of solutions for a large class of functional integral equations of Volterra type in two variables.     

The split common fixed point problem for generalized demimetric mappings in two Banach spaces

ABSTRACT

In this paper, we consider the split common fixed point problem for new demimetric mappings in two Banach spaces. Using the hybrid method, we prove a strong convergence theorem for finding a solution of the split common fixed point problem in two Banach spaces. Furthermore, using the shrinking projection method, we obtain another strong convergence theorem for finding a solution of the problem in two Banach spaces. Using these results, we obtain well-known and new strong convergence theorems in Hilbert spaces and Banach spaces.     

多目标规划的 Lagrange 对偶与标量化定理

定义与问题设 K(?)R~p 为内部非空的点锥,则 K 在 R~p 上确定了如下偏序:x≦K.y(?)y-x∈K,xk(?)}.     

Generalized vector mixed general quasi-variational-like inequalities in Hausdorff topological vector spaces

In this paper, we consider a generalized vector mixed general quasi-variational-like inequality in Hausdorff topological vector spaces. By using maximal element theorem, we prove existence theorems for two types of generalized vector mixed general quasi-variational-like inequalities without monotonicity and compactness.     

一类渐近线性双调和方程非平凡解的存在性

通过建立新空间H,证明了一个嵌入定理.进一步,利用该嵌入定理与山路引理得到了一类渐近线性双调和问题在空间H中非平凡解的存在性.     

一类带记忆项的非经典热方程的爆破问题

本文考虑了一类带记忆项的非经典热方程,证明解会在有限时间爆破,而且爆破只会发生在边界.主要结论是:首先利用Green函数与Banach压缩映射定理,建立了问题的经典解;其次,利用经典解,证明了解是有限时间爆破的;最后,证明了一个关于非经典热方程解的性质,利用这个性质,证明了解是在边界上爆破的.     

Variational and numerical analysis of a quasistatic viscoelastic contact problem with normal compliance and friction

In this paper, a class of generalized evolution variational inequalities arising in quasistatic friction contact problem for viscoelastic materials is introduced and studied. Under some suitable assumptions, we obtain an existence and uniqueness theorem of the solution for the generalized evolution variational inequalities by using Banach’s fixed point theorem. Moreover, we study two numerical approximation schemes of the problem: semidiscrete scheme and fully discrete scheme. For both schemes, we prove the existence of the solution and derive the error estimations.