scholarly journals Degree theory for Wiener maps

1986 ◽  
Vol 68 (3) ◽  
pp. 388-403 ◽  
Author(s):  
Ezra Getzler
Keyword(s):  
Degree Theory

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.

scholarly journals On resonant mixed Caputo fractional differential equations

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Assia Guezane-Lakoud ◽  
Adem Kılıçman
Keyword(s):  
Differential Equation ◽  
Fractional Derivatives ◽  
Existence Of Solutions ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Caputo Fractional Derivatives ◽  
At Resonance ◽  
Caputo Fractional Differential Equations ◽  
Fractional Differential ◽  
Problem At Resonance

Abstract The purpose of this study is to discuss the existence of solutions for a boundary value problem at resonance generated by a nonlinear differential equation involving both right and left Caputo fractional derivatives. The proofs of the existence of solutions are mainly based on Mawhin’s coincidence degree theory. We provide an example to illustrate the main result.

scholarly journals Existence and uniqueness criteria for the higher-order Hilfer fractional boundary value problems at resonance

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Yousef Gholami
Keyword(s):  
Boundary Value Problems ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Higher Order ◽  
Coupled Systems ◽  
At Resonance ◽  
Uniqueness Criteria ◽  
Fractional Boundary Value Problems

Abstract This investigation is devoted to the study of a certain class of coupled systems of higher-order Hilfer fractional boundary value problems at resonance. Combining the coincidence degree theory with the Lipschitz-type continuity conditions on nonlinearities, we present some existence and uniqueness criteria. Finally, to practically implement the obtained theoretical criteria, we give an illustrative application.

scholarly journals Permanence and Positive Periodic Solutions of a Discrete Delay Competitive System

2010 ◽  
Vol 2010 ◽  
pp. 1-22 ◽  
Author(s):  
Wenjie Qin ◽  
Zhijun Liu
Keyword(s):  
Periodic Solutions ◽  
Global Attractivity ◽  
Sufficient Conditions ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Discrete Delay ◽  
Positive Periodic Solutions ◽  
Competitive System ◽  
Discrete Function ◽  
Species Population

A discrete time non-autonomous two-species competitive system with delays is proposed, which involves the influence of many generations on the density of species population. Sufficient conditions for permanence of the system are given. When the system is periodic, by using the continuous theorem of coincidence degree theory and constructing a suitable Lyapunov discrete function, sufficient conditions which guarantee the existence and global attractivity of positive periodic solutions are obtained. As an application, examples and their numerical simulations are presented to illustrate the feasibility of our main results.

Homotopy and Degree Theory

2002 ◽  
pp. 159-204
Author(s):  
Antonio Villanacci ◽  
Laura Carosi ◽  
Pierluigi Benevieri ◽  
Andrea Battinelli
Keyword(s):  
Degree Theory

scholarly journals Existence and global stability of periodic solution for delayed discrete high-order Hopfield-type neural networks

2005 ◽  
Vol 2005 (3) ◽  
pp. 281-297 ◽  
Author(s):  
Hong Xiang ◽  
Ke-Ming Yan ◽  
Bai-Yan Wang
Keyword(s):  
Neural Networks ◽  
Periodic Solution ◽  
Global Stability ◽  
A Priori Estimates ◽  
A Priori ◽  
Sufficient Conditions ◽  
Coincidence Degree ◽  
Degree Theory ◽  
High Order ◽  
Priori Estimates

By using coincidence degree theory as well as a priori estimates and Lyapunov functional, we study the existence and global stability of periodic solution for discrete delayed high-order Hopfield-type neural networks. We obtain some easily verifiable sufficient conditions to ensure that there exists a unique periodic solution, and all theirs solutions converge to such a periodic solution.

scholarly journals Global Stability Analysis of a Nonautonomous Stage-Structured Competitive System with Toxic Effect and Double Maturation Delays

2014 ◽  
Vol 2014 ◽  
pp. 1-15 ◽  
Author(s):  
Chao Liu ◽  
Yuanke Li
Keyword(s):  
Global Stability ◽  
Toxic Effect ◽  
Sufficient Conditions ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Stage Structure ◽  
Positive Periodic Solution ◽  
Competitive System ◽  
Comparison Arguments ◽  
Double Time

We investigate a nonautonomous two-species competitive system with stage structure and double time delays due to maturation for two species, where toxic effect of toxin liberating species on nontoxic species is considered and the inhibiting effect is zero in absence of either species. Positivity and boundedness of solutions are analytically studied. By utilizing some comparison arguments, an iterative technique is proposed to discuss permanence of the species within competitive system. Furthermore, existence of positive periodic solutions is investigated based on continuation theorem of coincidence degree theory. By constructing an appropriate Lyapunov functional, sufficient conditions for global stability of the unique positive periodic solution are analyzed. Numerical simulations are carried out to show consistency with theoretical analysis.

Sign in / Sign up

Export Citation Format

Share Document