拓扑度计算及其应用

本文在文[1]的基础上,证明了一条coincidence度等于零的结果,此结果相当于Brower度与Leray-Schauder度的缺方向性质,利用此结果,将coincidence度与Banach空间中锥理论相结合,得出某一类算子方程具有非零正解的一些判别性条件,这对解决非线性常微分方程边值问题,具有一定作用。     

Coincidence Properties for Maps from the Torus to the Klein Bottle

The authors study the coincidence theory for pairs of maps from the Torus to the Klein bottle. Reidemeister classes and the Nielsen number are computed, and it is shown that any given pair of maps satisfies the Wecken property. The 1-parameter Wecken property is studied and a partial negative answer is derived. That is for all pairs of coincidence free maps a countable family of pairs of maps in the homotopy class is constructed such that no two members may be joined by a coincidence free homotopy.     

Coincidence Point Theorems,Intersection Theorems and Saddle Point Theorems on FC-spaces

In this paper, we first give the definitions of finitely continuous topological space and FC-subspace generated by some set, and obtain coincidence point theorem, whole intersection theorems and Ky Fan type matching theorems, and finally discuss the existence of saddle point as an application of coincidence point theorem.     

广义凸空间上的重合点和几乎相似重合点及其应用(英文)

We introduce the concept of a weakly G-quasiconvex map with respect to a map on generalized convex spaces and use the concept to prove coincidence point theorems and almost-like coincidence point theorems. As applications of the above results, we derive almost fixed point theorems and fixed point theorem. These main results generalize and improve some known results in the literature.     

COINCIDENCE THEOREMS IN PRODUCT G-CONVEX SPACES

By applying the technique of continuous partition of unity, some new coincidence theorems for a better admissible mapping and a family of set-valued mappings defined on the product G-convex spaces are proved. Theorems of this paper improve, unify and generalize many important coincidence theorems and collectively fixed point theorems in recent literature.     

Obstruction Theory and Coincidences in Positive Codimension

Let f, g ： X→Y be two maps between closed manifolds with dim X ≥ dim Y = n ≥ 3. We study the primary obstruction on（f, g） to deforming f and g to be coincidence free on the n-th skeleton of X. We give examples for which obstructions to deforming f and g to be coincidence free are detected by on （f, g）.     

MULTIPLE POSITIVE PERIODIC SOLUTIONS IN A IMPULSIVE PREDATOR-PREY SYSTEM WITH TYPEⅣFUNCTIONAL RESPONSES

The main purpose of this paper is to explore the existence of positive periodic solutions to impulsive predator-prey systems with typeⅣfunctional responses. Sufficient criteria are obtained for the existence of strictly positive periodic solutions.The approach is based on a continuation theorem in the coincidence degree theory as well as some prior estimates.This is also the first time that multiple positive periodic solutions are obtained using coincidence degree theory in impulsive ecological systems.     

Points of Coincidence and Common Fixed Points for Ⅱ-Expansive Mappings on Complex Valued Metric Spaces

We use the two mappings satisfying Ⅱ-expansive conditions on complex valued metric spaces to construct the convergent sequences and prove that the unique limit of the sequences is the point of coincidence or common fixed point of the two mappings.Also,we discuss the uniqueness of points of coincidence or common fixed points and give the existence theorems of unique fixed points.The obtained results generalize and improve the corresponding conclusions in references.     

PERIODIC SOLUTIONS FOR A LINARD-TYPE EQUATION WITH DELAYS

In this paper, we use the coincidence degree theory to establish new results on the existence of T-periodic solutions for the Lienard-type equation with delays.     

EXISTENCE OF POSITIVE PERIODIC SOLUTION TO A CLASS OF NEUTRAL DELAY COMPETITION MODEL

By means of the theory of coincidence degree, sufficient condition for the existence of positive periodic solution to certain neutral delay competition model is obtained.     

纯粹递归论在递归分析中的应用

本文利用纯粹递归论的近代结果研究了单位闭区间 I 上可计算实函数最大值点集中诸点的可计算度的结构。得到例如如下结果:1.对于任一度0<α≤0′,存在一个 I 上的递归实函数,它不具有递归的最大值点,但有度为α的最大位点;2.对于定义在 I 上的任一递归实函数,至少有一最大值点具有 r.e.度。文中顺便对 E.Specker 关于此问题的奠基性结果给出了一个直观自然的看法。     

模糊群决策结果的可信性评估

模糊数是群决策中常用的决策结果表达形式.研究了模糊群决策结果的可信性评估问题.认为群决策结果的可信性与模糊群决策结果的模糊度和一致度存在强相关,因此,模糊群决策结果可信性评估主要就是对群决策结果的模糊度和一致度的计算,创新提出了基于群隶属函数的模糊度和一致度的计算方法,并给出了基于模糊度和一致度的专家模糊数决策结果综合评价值的计算方法,最后,在此基础上求得专家模糊评估结果的可信度和群决策结果的可信度.     

EXISTENCE OF PERIODIC SOLUTIONS TO A KIND OF n-ORDER NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATION

By means of the continuation theorem of coincidence degree theory, we study a kind of n-order neutral functional differential equation. Some new results on the existence of periodic solutions are obtained.     

一类带有三维核的多点边值问题解的存在性(英文)

In this paper,a multi-point boundary value problems for a three order nonlinear deferential equation is considered.With the help of coincidence theorem due to Mawhin,a existence theorem is obtained.     

POSITIVE PERIODIC SOLUTIONS TO NEUTRAL RATIO-DEPENDENT PREDATOR-PREY SYSTEM

Using Mawhin's continuation theorem of coincidence degree theory,the existenceof periodic solutions to a neutral ratio-dependent predator-prey system is considered.The results in this paper generalize the corresponding results of the known literature.     

EXISTENCE OF PERIODIC SOLUTION TO GENERALIZED NEUTRAL LINARD DIFFERENTIAL EQUATION

In this paper, we consider a generalized neutral Li′enard differential equation. By applications of coincidence degree theory and some analysis skills, sufficient conditions for the existence of periodic solution is established.     

T-PERIODIC SOLUTION TO A TIME DELAY LINARD’S EQUATION

In this paper, a time delay Liénard’s equation is considered, by the coincidence degree theory. Sufficient conditions for the existence of at least one T-periodic solution are obtained.     

PERIODIC SOLUTIONS TO p-LAPLACIAN GENERALIZED LINARD EQUATION WITH DEVIATING ARGUMENTS

Using the theory of coincidence degree,we study a kind of periodic solutions to p-Laplacian generalized Liénard equation with deviating arguments. A result on the existence of periodic solutions is obtained.     

POSITIVE PERIODIC SOLUTIONS OF IMPULSIVE LATKA-VOLTERRA EQUATIONS

By using the continuation of coincidence degree theory, we study the periodic Lotka-Volterra equations with impulses, and some sufficient onditions for the existence of positive periodic solutions are obtained.     

PERIODIC SOLUTION TO A CLASS OF SECOND ORDER NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATION WITH A STATEMENT-DEPENDENT DEVIATION VARIABLE

We obtain sufficient conditions for the existence of periodic solution to a class of second order neutral functional differential equation,using continuation theorem of the coincidence degree.