scholarly journals Nonlinear Spectrum and Fixed Point Index for a Class of Decomposable Operators

Mathematics ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 278
Author(s):  
Shugui Kang ◽  
Yanlei Zhang ◽  
Wenying Feng
Keyword(s):  
Fixed Point ◽  
Fixed Point Index ◽  
Order Differential Equation ◽  
Spectral Interval ◽  
Point Index ◽  
Nonlinear Operators ◽  
Existence Of Positive Solutions ◽  
Separated Boundary Conditions ◽  
Decomposable Operators ◽  
Nonlinear Spectrum

We study a class of nonlinear operators that can be written as the composition of a linear operator and a nonlinear map. We obtain results on fixed point index based on parameters that are related to the definitions of nonlinear spectra. As a particular case, existence of positive solutions for a second-order differential equation with separated boundary conditions is proved. The result also provides a spectral interval for the corresponding Hammerstein integral operator.

scholarly journals Positive Solutions for a System of Hadamard-Type Fractional Differential Equations with Semipositone Nonlinearities

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-14 ◽  
Author(s):  
Youzheng Ding ◽  
Jiqiang Jiang ◽  
Donal O’Regan ◽  
Jiafa Xu
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Positive Solutions ◽  
Fractional Differential Equations ◽  
Fixed Point Index ◽  
Nonnegative Matrices ◽  
Point Index ◽  
Existence Of Positive Solutions ◽  
Fractional Differential

In this paper, we use the fixed-point index and nonnegative matrices to study the existence of positive solutions for a system of Hadamard-type fractional differential equations with semipositone nonlinearities.

scholarly journals A Generalization of Mahadevan's Version of the Krein-Rutman Theorem and Applications top-Laplacian Boundary Value Problems

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Yujun Cui ◽  
Jingxian Sun
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Boundary Value Problems ◽  
Fixed Point Index ◽  
Boundary Value ◽  
Point Index ◽  
Homogeneous Operator ◽  
Existence Of Positive Solutions ◽  
Positive Eigenfunction ◽  
Homogeneous Operators

We will present a generalization of Mahadevan’s version of the Krein-Rutman theorem for a compact, positively 1-homogeneous operator on a Banach space having the properties of being increasing with respect to a conePand such that there is a nonzerou∈P∖{θ}−Pfor whichMTpu≥ufor some positive constantMand some positive integerp. Moreover, we give some new results on the uniqueness of positive eigenvalue with positive eigenfunction and computation of the fixed point index. As applications, the existence of positive solutions forp-Laplacian boundary-value problems is considered under some conditions concerning the positive eigenvalues corresponding to the relevant positively 1-homogeneous operators.

The fixed-point index of nonlinear operators in Menger PN-spaces

2011 ◽  
Vol 90 (1-2) ◽  
pp. 94-101
Author(s):  
Qiuying Li ◽  
Chuanxi Zhu
Keyword(s):  
Fixed Point ◽  
Fixed Point Index ◽  
Point Index ◽  
Nonlinear Operators

EXISTENCE OF MULTIPLE POSITIVE SOLUTIONS FOR p-LAPLACIAN PROBLEMS WITH A GENERAL INDEFINITE WEIGHT

2008 ◽  
Vol 10 (03) ◽  
pp. 337-362 ◽  
Author(s):  
CHAN-GYUN KIM ◽  
YONG-HOON LEE
Keyword(s):  
Fixed Point ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Fixed Point Index ◽  
Singular Boundary ◽  
Multiple Positive Solutions ◽  
Singular Boundary Value Problems ◽  
Indefinite Weight ◽  
Point Index ◽  
Existence Of Positive Solutions

This paper studies the existence of positive solutions for a class of singular boundary value problems of p-Laplacian. By using Global Continuation Theorem and the fixed point index technique, criteria of the existence, multiplicity and nonexistence of positive solutions are established.

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 Green’s Function and Positive Solutions of a Third-Order Equation with Periodic Boundary Conditions

2020 ◽  
Vol 2020 ◽  
pp. 1-5
Author(s):  
Nickolai Kosmatov
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Positive Solutions ◽  
Fixed Point Index ◽  
Periodic Boundary ◽  
Order Differential Equation ◽  
Periodic Boundary Conditions ◽  
Order Equation ◽  
Point Index ◽  
Third Order

We apply the fixed point index to obtain positive solutions of a nonresonant periodic boundary value problem for a third-order differential equation u‴+ρ3u=λfu.

Positive Solutions for Nonlinear Lidstone Boundary Value Problems

2013 ◽  
Vol 313-314 ◽  
pp. 1201-1204 ◽  
Author(s):  
Lei Wang ◽  
Li Li
Keyword(s):  
Fixed Point ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Fixed Point Index ◽  
Existence Result ◽  
Boundary Value ◽  
Index Theorem ◽  
Point Index ◽  
Existence Of Positive Solutions ◽  
Fixed Point Index Theorem

In this paper, we consider the existence of positive solutions for nonlinear Lidstone boundary value problems. An new existence result is obtained by applying the fixed point index theorem.

Positive Solution of Nonlinear Two-Order Three-Point Boundary Value Problem for Difference Equation with Change of Sign

2014 ◽  
Vol 687-691 ◽  
pp. 1232-1236
Author(s):  
Chun Li Wang
Keyword(s):  
Fixed Point ◽  
Boundary Value Problem ◽  
Positive Solution ◽  
Fixed Point Index ◽  
Boundary Value ◽  
Index Theory ◽  
Point Boundary ◽  
Point Index ◽  
Fixed Point Index Theory ◽  
Existence Of Positive Solutions

In this paper we investigate the existence of positive solution of the following discrete two-order three-point boundary value problemWherandis sign-changing on . By using the fixed-point index theory, the existence of positive solutions for the above boundary value problem is obtained.

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