集值映射的 RS集逼近

本文研究了取值为 Banach空间中子集的上半连续的集值映射的 RS集逼近问题 ,给出了集值映 射用 RS集逼近的特征和唯一性结果 ,从而推广了他人的结果 .     

New uniqueness theorems for trigonometric series

A uniqueness theorem is proved for trigonometric series and another one is proved for multiple trigonometric series. A corollary of the second theorem asserts that there are two subsets of the -dimensional torus, the first having a countable number of points and the second having points such that whenever a multiple trigonometric series ``converges' to zero at each point of the former set and also converges absolutely at each point of the latter set, then that series must have every coefficient equal to zero. This result remains true if ``converges' is interpreted as any of the usual modes of convergence, for example as ``square converges' or as ``spherically converges.'

     

Abstract parabolic problems with critical nonlinearities and applications to Navier-Stokes and heat equations

We prove a local existence and uniqueness theorem for abstract parabolic problems of the type when the nonlinearity satisfies certain critical conditions. We apply this abstract result to the Navier-Stokes and heat equations.

     

Abstract Volterra operators

We propose a new general definition of Volterra operators. Several types of evolutionary operators, including Volterra ones in the sense of A.N. Tikhonov, satisfy this definition. For equations with generalized Volterra operators we introduce the notions of local, global, and maximally extended solutions. For solutions to nonlinear equations we formulate the existence, uniqueness, and extendability conditions. The theorems proved in this paper imply both known and new results on the solvability of concrete equations. We adduce an example of the application of obtained results to the study of the Cauchy problem for functional differential equations.     

A SECOND-ORDER PERIODIC BOUNDARY VALUE PROBLEM WITH SINGULAR AND DISCONTINUOUS NONLINEARITY

1. Introduction and Main ResultsIn recent years, singular nonlinear two-point boundary value problems have been studied. For details, see, for instance, [1--14] and references therein. However, the periodicboundary problems with singlllar and discontinuous nonlinearity are quite rarely studied.Motivated by [12,14], we study in this paper a periodic boundary value problem with singularand discontinuous nonlinearity of the form{;<;';<2;::<'> =:<u:>::<,.>,, 5 t 5 27, (1 1)where p is a positi…     

Banach空间中微分方程解的存在与唯一性

在一般Banach空间中,作者讨论了微分方程的初值问题u=f(t,u),u(0)=x0.在比文[6]中弱Carathodory条件更弱的情况下,不仅放宽了[6]中的一个重要不等式条件,还去掉了另一与之相关的不等式限制,仍获得了初值问题解的存在与唯一性及解的迭代逼近.对周期边值问题也获得了类似结果.     

Existence and uniqueness of solutions for singular integral equation

Using the mixed monotone method we establish existence and uniqueness results for a singular integral equation. The theorem obtained is very general and complements previous known results. The work was supported by the National Natural Science Foundation of China (No.10571021 and No.10701020) and Key Laboratory for Applied Statistics of MOE(KLAS) and Subject Foundation of Harbin University (No. HXK200714).     

Existence results for dynamic adhesive contact of a rod

The existence and uniqueness of the weak solution to the model for the dynamics of a viscoelastic rod which is in adhesive contact with an obstacle is established. The model consists of a hyperbolic equation for the vibrations of the rod coupled with a nonlinear ordinary differential equation (ODE) for the evolution of the bonding function. The model allows for failure, i.e., complete debonding, in finite time. The existence of the weak solution is established by using an existence result for ODEs and the Schauder fixed-point theorem. The limit of an elastic rod when the viscosity vanishes is studied, too.     

Chromatic Uniqueness of a Family of K_4-Homeomorphs

§ 1.Ｉｎｔｒｏｄｕｃｔｉｏｎ　Ａｌｌｇｒａｐｈｓｃｏｎｓｉｄｅｒｅｄｉｎｔｈｉｓｐａｐｅｒａｒｅｆｉｎｉｔｅ,ｕｎｄｉｒｅｃｔｅｄ ,ｕｎｌｏｏｐｅｄａｎｄｓｉｍｐｌｅｇｒａｐｈｓ.ＷｅｄｅｎｏｔｅｔｈｅｃｈｒｏｍａｔｉｃｐｏｌｙｎｏｍｉａｌｏｆａｇｒａｐｈＧｂｙＰ(Ｇ ,λ)ｏｒＰ(Ｇ) .ＷｅｓａｙｇｒａｐｈｓＧａｎｄＨｔｏｂｅｃｈｒｏｍａｔｉａｌｌｙｅｑｕｉｖａｌｅｎｔｉｆＰ(Ｇ) =Ｐ(Ｈ) .ＴｈｅｃｈｒｏｍａｔｉｃｕｎｉｑｕｅｎｅｓｓｏｆａｇｒａｐｈＧｉｓｅｓｔａｂｌｉｓｈｅｄｉｆｉｔｃａｎｂｅｄｅｄ…     

ON GUNDERSEN＇S QUESTION FOR THE UNICITY OF MEROMORPHIC FUNCTIONS

The uniqueness of meromoRphic functions that share four values are investigated, some results are obtained to show that if two nonconstant entire functions share three finite values IM, then the functions necessarily share all three values CM.