A fixed point index approach to some differential equations

1989 ◽  
pp. 9-14 ◽  
Author(s):  
R. Bielawski ◽  
L. Górniewicz
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Fixed Point Index ◽  
Point Index ◽  
Index Approach

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 Fixed point index of iterations of local homeomorphisms of the plane: a Conley index approach

Topology ◽  
2002 ◽  
Vol 41 (6) ◽  
pp. 1199-1212 ◽  
Author(s):  
Francisco R. Ruiz del Portal ◽  
José M. Salazar
Keyword(s):  
Fixed Point ◽  
Fixed Point Index ◽  
Conley Index ◽  
Point Index ◽  
Index Approach

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 Fixed point index approach for solutions of variational inequalities

2005 ◽  
Vol 2005 (12) ◽  
pp. 1879-1887 ◽  
Author(s):  
Yisheng Lai ◽  
Yuanguo Zhu ◽  
Yinbing Deng
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Variational Inequalities ◽  
Fixed Point Index ◽  
Reflexive Banach Space ◽  
The Other ◽  
Multivalued Mappings ◽  
Point Index ◽  
Upper Semicontinuous ◽  
Index Approach

By using fixed point index approach for multivalued mappings, the existence of nonzero solutions for a class of generalized variational inequalities is studied in reflexive Banach space. One of the mappings concerned here is coercive or monotone and the other is set-contractive or upper semicontinuous.

On Fixed Point Index Formula and its Applications in Dynamics

2013 ◽  
Vol 13 (2) ◽  
Author(s):  
Klaudiusz Wójcik
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Chaotic Dynamics ◽  
Fixed Point Index ◽  
Topological Method ◽  
Index Formula ◽  
Point Index

AbstractThe aim of this note is to present a generalization of the topological method for detecting chaotic dynamics in a periodic local processes generated by non-autonomous ordinary differential equations, based on the notion of periodic segments.

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.

scholarly journals Multiple Positive Solutions for a System of Nonlinear Caputo-Type Fractional Differential Equations

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Hongyu Li ◽  
Yang Chen
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Positive Solutions ◽  
Fractional Differential Equations ◽  
Fixed Point Index ◽  
Index Theory ◽  
Multiple Positive Solutions ◽  
Point Index ◽  
Fixed Point Index Theory ◽  
Fractional Differential

By using fixed-point index theory, we consider the existence of multiple positive solutions for a system of nonlinear Caputo-type fractional differential equations with the Riemann-Stieltjes boundary conditions.

scholarly journals Nontrivial Solutions of Systems of Perturbed Hammerstein Integral Equations with Functional Terms

Mathematics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 330
Author(s):  
Gennaro Infante
Keyword(s):  
Fixed Point ◽  
Boundary Conditions ◽  
Integral Equations ◽  
General Class ◽  
Fixed Point Index ◽  
Nontrivial Solutions ◽  
Point Index ◽  
Hammerstein Integral Equations ◽  
Functional Boundary ◽  
Functional Boundary Conditions

We discuss the solvability of a fairly general class of systems of perturbed Hammerstein integral equations with functional terms that depend on several parameters. The nonlinearities and the functionals are allowed to depend on the components of the system and their derivatives. The results are applicable to systems of nonlocal second order ordinary differential equations subject to functional boundary conditions, this is illustrated in an example. Our approach is based on the classical fixed point index.

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