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On the fixed point index and fixed point Theorems for Semi-closed 1-set-contraction Mapping

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江西师范大学学报(自然科学版) 1991年第1期 1-9页

作者： Li Ouozhm (Jianmgai Normal University) Chen Yucking (Fordham University U. S. A)

In this paper we define the fixed point index of semi-closed 1-set-contraction mappings by new way and we use the fixed point index to prove some new fixed point theorems of semi-closed 1-setcontraction mappings including theorems on multiple positive fixed points,which extend main results of [1,2,3,7]. This paper is a continuation of Li[12].

关键词： Semi-closed 1-set-contraction mapping fixed point index fixed point

Existence of Monotone Positive Solution for a Fourth-Order Three-point BVP with Sign-Changing Green’s Function

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Open Journal of Applied Sciences 2024年第1期14卷 63-69页

作者： Junrui Yue Yun Zhang Qingyue Bai Computer Information Engineering Institute Shanxi Technology and Business College Taiyuan China Shanxi Technology and Business College Taiyuan China

This paper is concerned with the following fourth-order three-point boundary value problem , where , we discuss the existence of positive solutions to the above problem by applying to the fixed point theory in cones a... 详细信息

关键词： Fourth-Order Three-point Boundary Value Problem Sign-Changing Green’s Function fixed point index Iterative Technique Monotone Positive Solution Existence

On fixed point index and fixed point Theorems for Multivalued Semi-closed 1-set-contraction Mappings

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江西师范大学学报(自然科学版) 1991年第4期 294-297+305页

作者： Li Guozhen (Dept. of Math.)

Fitzpatrick P M and Petryshyn W V studied fixed point index and fixed point theorems of multivalued condensing mappings.The aim of this paper is to give a concept of multivalued semi-closed 1-set-contraction mapping which is a more genere.i mapping and to define its fixed point index,and then we prove some fixed point theorems to extend some Petryshyn’ s results.

关键词： fixed point index fixed point theorems

Nonexistence and Existence of Multiple Positive Solutions for Superlinear Three-point Boundary Value Problems via index Theory

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Acta Mathematicae Applicatae Sinica 2008年第4期24卷 529-540页

作者： Bao-qiang Yan Donal O'Regan Ravi P. Agarwal Department of Mathematics Shandong Normal University Jinan 250014 China Department of Mathematics National University of Ireland Galway Ireland Department of Mathematical Science Florida Institute of Technology Melbourne Florida 32901 USA

This paper discusses both the nonexistence of positive solutions for second-order three-point boundary value problems when the nonlinear term f（t, x, y） is superlinear in y at y = 0 and the existence of multiple positive solutions for second-order three-point boundary value problems when the nonlinear term f（t, x,y） is superlinear in x at ＋∞.

关键词： Three-point boundary value problems cone fixed point index

Positive Solutions of Fourth-Order Equations under Nonlocal Boundary Value Conditions of Sturm-Liouville Type

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Journal of Mathematical Research with Applications 2023年第1期43卷 91-100页

作者： Chunlei SONG Wei CHEN Guowei ZHANG Department of Mathematics Northeastern University

In this paper, we study the fourth-order problem with the first and second derivatives in nonlinearity under nonlocal boundary value conditions of Sturm-Liouville type involving Stieltjes integrals. Some inequality conditions on nonlinearity are presented that guarantee the existence of positive solutions to the problem by the theory of fixed point index on a special cone. Some examples are provided to support the main results under mixed boundary conditions containing multi-point with sign-changing coefficients and integral with sign-changing kernel.

关键词： positive solution fixed point index cone

A Multiplicity Result of Positive Solutions for a Class of Multi-parameter Ordinary Differential Systems

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Acta Mathematicae Applicatae Sinica 2012年第4期28卷 653-662页

作者： Xi-you CHENG Xiao-lin YAN School of Mathematics and Statistics Lanzhou University School of Science Tianjin Polytechnic University

In this paper, we establish a result of Leray-Schauder degree on the order interval which is induced by a pair of strict lower and upper solutions for a system of second-order ordinary differential equations. As applications, we prove the global existence of positive solutions for a multi-parameter system of second-order ordinary differential equations with respect to parameters. The discussion is based on the result of Leray- Schauder degree on the order interval and the fixed point index theory in cones.

关键词： positive solution ordinary differential system fixed point index

Existence of Multiple fixed points for Nonlinear Operators and Applications

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Acta Mathematica Sinica,English Series 2008年第7期24卷 1079-1088页

作者： Jing Xian SUN Ke Mei ZHANG Department of Mathematics Xuzhou Normal University Xuzhou 221116 P. R. China Department of Mathematics Qufu Normal University Qufu 273165 P. R. China

In this paper, by the fixed point index theory, the number of fixed points for sublinear and asymptotically linear operators via two coupled parallel sub-super solutions is studied. Under suitable conditions, the existence of at least nine or seven distinct fixed points for sublinear and asymptotically linear operators is proved. Finally, the theoretical results are applied to a nonlinear system of Hammerstein integral equations.

关键词： cone fixed point index parallel sub-super solutions

MULTIPLE POSITIVE SOLUTIONS FOR SUPERLINEAR SECOND ORDER SINGULAR BOUNDARY VALUE PROBLEMS WITH DERIVATIVE DEPENDENCE

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Acta Mathematica Scientia 2008年第4期28卷 851-864页

作者：闫宝强 Department of Mathematics Shandong Normal University School of Mathematics Trinity College

The existence of at least two positive solutions is presented for the singular second-order boundary value problem{1/p（t）（ p（t）x′（t））′＋Φ（t）f（t,x（t）,p（t）x′（t））=0,0〈t〈1, limt→0 p（t）x′（t）=... 详细信息

关键词： Boundary value problems singularity fixed point index

TWO POSITIVE SOLUTIONS TO THREE-point SINGULAR BOUNDARY VALUE PROBLEMS

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Acta Mathematica Scientia 2011年第1期31卷 29-38页

作者：李宇华梁占平 School of Mathematical Sciences Shanxi University

In this article, we consider the existence of two positive solutions to nonlinear second order three-point singular boundary value problem： -u′′（t） = λf（t, u（t）） for all t ∈ （0, 1） subjecting to u（0） = 0 and αu（η） = u（1）, where η ∈ （0, 1）, α ∈ [0, 1）, and λ is a positive parameter. The nonlinear term f（t, u） is nonnegative, and may be singular at t = 0, t = 1, and u = 0. By the fixed point index theory and approximation method, we establish that there exists λ＊ ∈ （0, ＋∞], such that the above problem has at least two positive solutions for any λ ∈ （0, λ＊） under certain conditions on the nonlinear term f.

关键词： Three-point singular boundary value problem positive solutions fixed point index