随机凝聚型广义内向映射的随机不动点指数

本文引进了随机广义内向映射的随机不动点指数，利用该不动点指数我们得到了一些新的随机不动点定理，并给出了其一个应用．     

Existence of nonzero positive solutions of systems of second order

Existence of nonzero positive solutions  of systems of second order elliptic boundary value problems under sublinear conditions is obtained. The methodology is to establish a new result on existence of nonzero positive solutions of a fixed point equation in real Banach spaces by using the well-known theory of fixed point index for compact maps defined on cones, where the fixed point equation involves composition of a compact linear operator and a continuous nonlinear map. The conditions imposed on the nonlinear maps involve the spectral radii of the compact linear operators. Moreover, the nonlinear maps are not required to be increasing in  ordered Banach spaces.     

非锥映射的不动点指数计算及其应用

本文应用锥理论获得了一类不是锥映射的非线性算子不动点指数计算的若干结果,并将所得结果应用于非线性椭圆型偏微分方程边值问题.     

Banach空间中二阶三点奇异边值问题的多个正解

通过构造一个特殊的锥,利用锥上的不动点指数,研究了Banach空间中二阶三点奇异边值问题多个正解的存在性.     

Multiple solutions for fourth-order boundary value problem

In this paper, we study the existence and multiplicity of nontrivial solutions for the fourth-order two point boundary value problems. Making use of the theory of fixed point index in cone and Leray-Schauder degree, under general conditions on nonlinearity, we prove that there exist at least six different nontrivial solutions for the fourth-order two point boundary value problems. Furthermore, if the nonlinearity is odd, we obtain that there exist at least eight different nontrivial solutions.     

锥上减映象的不动点及其在非局部边值问题中的应用

研究锥上一类减映象,得到这类映象不动点的存在性、唯一性和迭代序列的收敛性.其结果在二阶非局部边值问题中得到应用.     

带两个参数四阶边值问题的正解与多解性

本文通过计算锥上的算子不动点指数,证明了一类含有两个参数的四阶微分方程的两点边值问题的一个和两个正解的存在性．     

A fixed point index for generalized inward mappings of condensing type

A fixed point index is defined for mappings defined on a cone which do not necessarily take their values in but satisfy a weak type of boundary condition called generalized inward. This class strictly includes the well-known weakly inward class. New results for existence of multiple fixed points are established.

     

FIXED POINTS FOR WEAKLY INWARD MAPPINGS IN BANACH SPACES (Ⅱ)

S. Hu and Y. Sun[1] defined the fixed point index for weakly inward mappings, investigated its properties and studied fixed points for such mappings. In this paper, following S. Hu and Y. Sun, we further investigate boundary conditions, under which the fixed point index for i(A,Ω, p) is equal to nonzero, where i(A,Ω, p) is the completely continuous and weakly inward mapping. Correspondingly, we can obtain many new fixed point the-orems of the completely continuous and weakly inward mapping, which generalize...     

The Existence and Multiplicity of Positive Solutions for a Third—order Three—point Boundary Value Problem

The existence of n positive solutions for a class of third-order three-point boundary value problems is investigated,where n is an arbitrary natural number,The main tool is Krasnosel‘skii fixed point theorem on the cone.     

Fixed points and graph images for minimal maps on the once punctured torus

A fixed point detection theorem for a family of maps defined on the once punctured torus is proved. As a consequence, we produce an example of a homotopy class [f] of self-maps on the once punctured torus that illustrates the following: (i) there is a map in the homotopy class that has no fixed points, and (ii) if the image of f lies in a 1-complex that embeds as a homotopy equivalence, then f must have a fixed point.     

Singular multipoint impulsive boundary value problem with p-Laplacian operator

In this paper, we obtain the existence of multiple positive solutions for a class of multipoint impulsive boundary value problem with p-Laplacian operator, where the nonlinearity may be singular on t=0, 1 and u=0. The main tool is the classical fixed point index theorem for compact maps.     

2n阶两点边值问题的多重非平凡解

本文主要研究2n阶两点边值问题的多重非平凡解的存在性．利用不动点指数理论和Leray-schauder度,在一般的非线性条件下,证明了2n阶两点边值问题至少有六个非平凡解的存在性．而且,如果非线性项是奇函数,则至少有八个非平凡解的存在．     

Existence and localization of positive solutions for a nonlocal BVP arising in chemical reactor theory

We discuss the existence of positive solutions of a nonlocal boundary value problem that models a chemical tubular reactor. Our approach allows us to deal with a wide range of parameters, nonlocal conditions and to provide upper and lower bounds for the solutions. We make use of the theory of fixed point index for compact maps. Some examples are presented to illustrate the theory.     

一类分数阶微分方程边值问题的三个正解

利用锥上Avery-Peterson不动点定理,研究了一类分数阶微分方程积分边值问题正解的存在性,给出了该边值问题至少存在三个正解的充分条件.     

弱内向型集压缩映射的正不动点和正特征元

本文建立了弱内向型集压缩映射的范数压缩与扩张型正不动点定理，并获得关于正特征元的一些结果．     

混合单调算子的两点拉伸型不动点定理

本文首次提出了混合单调算子不动点的两点拉伸型条件.同时,利用锥映象的不动点指数理论建立了一类特殊的两点拉伸型混合单调算子的不动点存在性定理,并将所得结论应用于带有超线性项的积分方程与微分方程上,得到了新的结论.因而在本质上推进了混合单调算子不动点问题的研究.     

一类微分方程组的非齐次Sturm-Liouville边值问题解的存在性

在允许非线性项变号的情况下,利用锥上不动点定理,讨论了一类二阶非线性微分方程组的非齐次Sturm-Liouville边值问题解的存在性,得到了至少一个解及正解存在的多个存在性定理．     

四阶微分方程奇异边值问题的正解

本文利用锥上的不动点指数理论,在更一般的边界条件下讨论了一类四阶奇异边值问题正解的存在性并给出了应用．     

Multiple solutions of singular boundary value problems for differential systems

By constructing a special cone and using fixed point index theory in cone, this paper investigates the existence of multiple solutions of singular boundary value problems for differential systems.