scholarly journals A degree theory for compact perturbations of properC1Fredholm mappings of index0

2005 ◽  
Vol 2005 (7) ◽  
pp. 707-731 ◽  
Author(s):  
Patrick J. Rabier ◽  
Mary F. Salter
Keyword(s):  
Banach Spaces ◽  
Global Bifurcation ◽  
Degree Theory ◽  
Bifurcation Theorem ◽  
Compact Perturbations ◽  
One To One ◽  
Domain Property

We construct a degree for mappings of the formF+Kbetween Banach spaces, whereFisC1Fredholm of index0andKis compact. This degree generalizes both the Leray-Schauder degree whenF=Iand the degree forC1Fredholm mappings of index0whenK=0. To exemplify the use of this degree, we prove the “invariance-of-domain” property whenF+Kis one-to-one and a generalization of Rabinowitz's global bifurcation theorem for equationsF(λ,x)+K(λ,x)=0.

scholarly journals A global bifurcation theorem for critical values in Banach spaces

2018 ◽  
Vol 198 (3) ◽  
pp. 773-794
Author(s):  
Pablo Amster ◽  
Pierluigi Benevieri ◽  
Julián Haddad
Keyword(s):  
Banach Spaces ◽  
Global Bifurcation ◽  
Critical Values ◽  
Bifurcation Theorem

scholarly journals Existence of solutions for functional boundary value problems at resonance on the half-line

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Bingzhi Sun ◽  
Weihua Jiang
Keyword(s):  
Boundary Value Problems ◽  
Banach Spaces ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Half Line ◽  
Projection Scheme ◽  
At Resonance ◽  
Functional Boundary

Abstract By defining the Banach spaces endowed with the appropriate norm, constructing a suitable projection scheme, and using the coincidence degree theory due to Mawhin, we study the existence of solutions for functional boundary value problems at resonance on the half-line with $\operatorname{dim}\operatorname{Ker}L = 1$ dim Ker L = 1 . And an example is given to show that our result here is valid.

Degree theory for mappings in non-reflexive banach spaces

2008 ◽  
Vol 202 (1) ◽  
pp. 229-232 ◽  
Author(s):  
Fulong Wang ◽  
Yuqing Chen ◽  
Donal O’Regan
Keyword(s):  
Banach Spaces ◽  
Degree Theory ◽  
Reflexive Banach Spaces

scholarly journals Stability and Hopf-Bifurcation Analysis of Delayed BAM Neural Network under Dynamic Thresholds

2009 ◽  
Vol 14 (4) ◽  
pp. 435-461 ◽  
Author(s):  
P. D. Gupta ◽  
N. C. Majee ◽  
A. B. Roy
Keyword(s):  
Hopf Bifurcation ◽  
Periodic Solutions ◽  
Global Bifurcation ◽  
Distributed Delay ◽  
Degree Theory ◽  
Homotopy Invariance ◽  
Normal Form Theory ◽  
Form Theory ◽  
Bam Neural Network ◽  
Uniqueness Of Equilibrium

In this paper the dynamics of a three neuron model with self-connection and distributed delay under dynamical threshold is investigated. With the help of topological degree theory and Homotopy invariance principle existence and uniqueness of equilibrium point are established. The conditions for which the Hopf-bifurcation occurs at the equilibrium are obtained for the weak kernel of the distributed delay. The direction and stability of the bifurcating periodic solutions are determined by the normal form theory and central manifold theorem. Lastly global bifurcation aspect of such periodic solutions is studied. Some numerical simulations for justifying the theoretical analysis are also presented.

scholarly journals A global bifurcation theorem for Darwinian matrix models

2016 ◽  
Vol 22 (8) ◽  
pp. 1114-1136 ◽  
Author(s):  
Emily P. Meissen ◽  
Kehinde R. Salau ◽  
Jim M. Cushing
Keyword(s):  
Matrix Models ◽  
Global Bifurcation ◽  
Bifurcation Theorem

scholarly journals Existence of Positive Solutions of a Discrete Elastic Beam Equation

2010 ◽  
Vol 2010 ◽  
pp. 1-15 ◽  
Author(s):  
Ruyun Ma ◽  
Jiemei Li ◽  
Chenghua Gao
Keyword(s):  
Positive Solutions ◽  
Fourth Order ◽  
Nonlinear Boundary ◽  
Global Bifurcation ◽  
Elastic Beam ◽  
Beam Equation ◽  
Nonlinear Boundary Value Problems ◽  
Order Difference ◽  
Bifurcation Theorem ◽  
Existence Of Positive Solutions

LetTbe an integer withT≥5and letT2={2,3,…,T}. We consider the existence of positive solutions of the nonlinear boundary value problems of fourth-order difference equationsΔ4u(t−2)−ra(t)f(u(t))=0,t∈T2,u(1)=u(T+1)=Δ2u(0)=Δ2u(T)=0, whereris a constant,a:T2→(0,∞),  and  f:[0,∞)→[0,∞)is continuous. Our approaches are based on the Krein-Rutman theorem and the global bifurcation theorem.

scholarly journals Impulsive Problems for Fractional Differential Equations with Functional Boundary Value Conditions at Resonance

2019 ◽  
Vol 2019 ◽  
pp. 1-12
Author(s):  
Bingzhi Sun ◽  
Shuqin Zhang ◽  
Weihua Jiang
Keyword(s):  
Differential Equations ◽  
Banach Spaces ◽  
Fractional Differential Equations ◽  
Boundary Value ◽  
Degree Theory ◽  
At Resonance ◽  
Impulsive Problems ◽  
Functional Boundary ◽  
Fractional Differential

We establish novel results on the existence of impulsive problems for fractional differential equations with functional boundary value conditions at resonance with dim⁡Ker L=1. Our results are based on the degree theory due to Mawhin, which requires appropriate Banach spaces and suitable projection schemes.

Sign in / Sign up

Export Citation Format

Share Document