scholarly journals Fixed point index for composite type maps

2009 ◽  
Vol 3 (2) ◽  
pp. 224-235
Author(s):  
Donal O'Regan
Keyword(s):  
Fixed Point ◽  
Fixed Point Index ◽  
Fixed Point Theorems ◽  
Index Theory ◽  
Point Index ◽  
Composite Type

An index theory is presented for compact absorbing contractive Jc or SJc maps and several new fixed point theorems are given for such maps.

scholarly journals Eigenvalue of Coupled Systems for Hammerstein Integral Equation with Two Parameters

2011 ◽  
Vol 2011 ◽  
pp. 1-11
Author(s):  
Wanjun Li
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Positive Solutions ◽  
Fixed Point Index ◽  
Index Theory ◽  
Coupled Systems ◽  
Point Index ◽  
Hammerstein Integral Equation ◽  
Fixed Point Index Theory ◽  
Two Parameters

By using the fixed-point index theory, we discuss the existence, multiplicity, and nonexistence of positive solutions for the coupled systems of Hammerstein integral equation with parameters.

scholarly journals A-properness and fixed point theorems for dissipative type maps

1999 ◽  
Vol 4 (2) ◽  
pp. 83-100 ◽  
Author(s):  
K. Q. Lan ◽  
J. R. L. Webb
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Fixed Point Index ◽  
Fixed Point Theorems ◽  
Duality Mapping ◽  
Uniformly Convex ◽  
Point Index ◽  
Weakly Inward ◽  
Convex Subsets

We obtain newA-properness results for demicontinuous, dissipative type mappings defined only on closed convex subsets of a Banach spaceXwith uniformly convex dual and which satisfy a property called weakly inward. The method relies on a new property of the duality mapping in such spaces. New fixed point results are obtained by utilising a theory of fixed point index.

scholarly journals Positive Solutions for a Class of Fourth-Order Boundary Value Problems in Banach Spaces

2011 ◽  
Vol 2011 ◽  
pp. 1-8
Author(s):  
Jingjing Cai ◽  
Guilong Liu
Keyword(s):  
Fixed Point ◽  
Banach Spaces ◽  
Positive Solutions ◽  
Fourth Order ◽  
Fixed Point Index ◽  
Boundary Value ◽  
Index Theory ◽  
Point Index ◽  
Fixed Point Index Theory ◽  
Existence And Nonexistence

Using a specially constructed cone and the fixed point index theory, this work shows existence and nonexistence results of positive solutions for fourth-order boundary value problem with two different parameters in Banach spaces.

Positive Radial Solutions for Elliptic Systems with Nonlocal Conditions

2012 ◽  
Vol 204-208 ◽  
pp. 4800-4808
Author(s):  
Sheng Li Xie
Keyword(s):  
Fixed Point ◽  
Elliptic System ◽  
Fixed Point Index ◽  
Nonlocal Conditions ◽  
Elliptic Systems ◽  
Index Theory ◽  
Point Index ◽  
Radial Solutions ◽  
Fixed Point Index Theory ◽  
Positive Radial Solutions

By using fixed point index theory,we study the existence of positive radial solutions and multiple positive radial solutions for the elliptic system with nonlocal conditions. Our results extend and improve some existing ones.

scholarly journals Application of Fixed-Point Index Theory for a Nonlinear Fractional Boundary Value Problem with an Advanced Argument

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Li Wu ◽  
Chuanzhi Bai
Keyword(s):  
Fixed Point ◽  
Boundary Value Problem ◽  
Fixed Point Index ◽  
Boundary Value ◽  
Index Theory ◽  
Fractional Boundary Value Problem ◽  
Point Index ◽  
Advanced Argument ◽  
Fixed Point Index Theory ◽  
Existence Of Positive Solutions

In this paper, we investigate the existence of positive solutions of a class of fractional three-point boundary value problem with an advanced argument by using fixed-point index theory. Our results improve and extend some known results in the literature. Two examples are given to demonstrate the effectiveness of our results.

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