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 Existence, Nonexistence and Multiplicity Results for Positive Radial Solutions of n−dimensional Elliptic System

2021 ◽  
pp. 35-45
Author(s):  
Yalin Shen
Keyword(s):  
Elliptic System ◽  
Positive Solutions ◽  
Fixed Point Index ◽  
Information Science ◽  
Elliptic Systems ◽  
Point Index ◽  
Radial Solutions ◽  
Multiplicity Results ◽  
Positive Radial Solutions ◽  
Multiplicity Of Positive Solutions

Aims/ Objectives: In this paper, we study the existence, nonexistence and multiplicity of positive solutions to the n−dimensional elliptic system  systems have been widely studied, but there is relatively little research on n-dimensional elliptic systems. We are very interested in this subject and want to study it. We give new conclusions on the existence, nonexistence and multiplicity of positive solutions for the n-dimensional elliptic system. Study Design: Study on the existence, nonexistence and multiplicity of positive solutions. Place and Duration of Study: School of Applied Science, Beijing Information Science & Technology University, September 2019 to present. Methodology: We prove the existence, nonexistence and multiplicity of positive solutions by the results of fixed point index. Results: We give new conclusions of existence, nonexistence and multiplicity of positive solutionsfor the system. Conclusion: We prove the existence, nonexistence and multiplicity of positive solutions to the n-dimensional elliptic system   and give new conclusions.

scholarly journals On Positive Radial Solutions for a Class of Elliptic Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-11
Author(s):  
Ying Wu ◽  
Guodong Han
Keyword(s):  
Fixed Point Index ◽  
Nonlinear Term ◽  
Elliptic Boundary ◽  
Index Theory ◽  
First Eigenvalue ◽  
Radial Solutions ◽  
Elliptic Boundary Value ◽  
Existence And Multiplicity ◽  
Fixed Point Index Theory ◽  
Positive Radial Solutions

A class of elliptic boundary value problem in an exterior domain is considered under some conditions concerning the first eigenvalue of the relevant linear operator, where the variables of nonlinear termfs,uneed not to be separated. Several new theorems on the existence and multiplicity of positive radial solutions are obtained by means of fixed point index theory. Our conclusions are essential improvements of the results in Lan and Webb (1998), Lee (1997), Mao and Xue (2002), Stańczy (2000), and Han and Wang (2006).

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 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.

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.

scholarly journals On fixed point index theory for the sum of operators and applications to a class of ODEs and PDEs

2021 ◽  
Vol 22 (2) ◽  
pp. 259
Author(s):  
Svetlin Georgiev Georgiev ◽  
Karima Mebarki
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Fixed Point Index ◽  
Index Theory ◽  
Point Index ◽  
First Order ◽  
Fixed Point Index Theory ◽  
Existence Of Positive Solutions ◽  
Theoretical Results ◽  
Positive Half

The aim of this work is two fold: first  we  extend some results concerning the computation of the fixed point index for the sum of an expansive mapping and a $k$-set contraction  obtained in \cite{DjebaMeb, Svet-Meb}, to  the case of the sum $T+F$, where $T$ is a mapping such that $(I-T)$ is Lipschitz invertible and $F$ is a $k$-set contraction.  Secondly, as  illustration of some our theoretical results,  we study  the existence of positive solutions  for two classes of differential equations, covering a class of first-order ordinary differential equations (ODEs for short) posed on the positive half-line as well as  a class of  partial differential equations (PDEs for short).

scholarly journals On Six Solutions form-Point Differential Equations System with Two Coupled Parallel Sub-Super Solutions

2012 ◽  
Vol 2012 ◽  
pp. 1-15
Author(s):  
Jian Liu ◽  
Hua Su ◽  
Shuli Wang
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Fixed Point Index ◽  
Index Theory ◽  
Second Order ◽  
Point Index ◽  
Fixed Point Index Theory

Under the assumption of two coupled parallel subsuper solutions, the existence of at least six solutions for a kind of second-orderm-point differential equations system is obtained using the fixed point index theory. As an application, an example to demonstrate our result is given.

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