scholarly journals Mawhin’s Continuation Technique for a Nonlinear BVP of Variable Order at Resonance via Piecewise Constant Functions

2021 ◽  
Vol 5 (4) ◽  
pp. 216
Author(s):  
Shahram Rezapour ◽  
Mohammed Said Souid ◽  
Sina Etemad ◽  
Zoubida Bouazza ◽  
Sotiris K. Ntouyas ◽  
...  
Keyword(s):  
Existence Of Solutions ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Variable Order ◽  
Mawhin’S Continuation Theorem ◽  
Piecewise Constant ◽  
At Resonance ◽  
Piecewise Constant Functions ◽  
The Given ◽  
Continuation Technique

In this paper, we establish the existence of solutions to a nonlinear boundary value problem (BVP) of variable order at resonance. The main theorem in this study is proved with the help of generalized intervals and piecewise constant functions, in which we convert the mentioned Caputo BVP of fractional variable order to an equivalent standard Caputo BVP at resonance of constant order. In fact, to use the Mawhin’s continuation technique, we have to transform the variable order BVP into a constant order BVP. We prove the existence of solutions based on the existing notions in the coincidence degree theory and Mawhin’s continuation theorem (MCTH). Finally, an example is provided according to the given variable order BVP to show the correctness of results.

scholarly journals Existence of Solutions for Fractional Multi-Point Boundary Value Problems on an Infinite Interval at Resonance

Mathematics ◽  
2020 ◽  
Vol 8 (1) ◽  
pp. 126
Author(s):  
Wei Zhang ◽  
Wenbin Liu
Keyword(s):  
Boundary Value Problems ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Existence Results ◽  
Infinite Interval ◽  
Point Boundary ◽  
At Resonance ◽  
The Given

This paper aims to investigate a class of fractional multi-point boundary value problems at resonance on an infinite interval. New existence results are obtained for the given problem using Mawhin’s coincidence degree theory. Moreover, two examples are given to illustrate the main results.

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 The Existence of Solutions for a Nonlinear Fractional Multi-Point Boundary Value Problem at Resonance

2011 ◽  
Vol 2011 ◽  
pp. 1-14 ◽  
Author(s):  
Xiaoling Han ◽  
Ting Wang
Keyword(s):  
Boundary Value Problem ◽  
Existence Result ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Existence Of Solution ◽  
At Resonance ◽  
Fractional Differential ◽  
Multipoint Boundary Value Problem

We discuss the existence of solution for a multipoint boundary value problem of fractional differential equation. An existence result is obtained with the use of the coincidence degree theory.

scholarly journals The Existence of Solutions for Four-Point Coupled Boundary Value Problems of Fractional Differential Equations at Resonance

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Yumei Zou ◽  
Lishan Liu ◽  
Yujun Cui
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Fractional Differential Equations ◽  
Existence Of Solutions ◽  
Existence Theorems ◽  
Boundary Value ◽  
Coincidence Degree ◽  
Degree Theory ◽  
At Resonance ◽  
Fractional Differential

A four-point coupled boundary value problem of fractional differential equations is studied. Based on Mawhin’s coincidence degree theory, some existence theorems are obtained in the case of resonance.

scholarly journals Existence of Solutions for Two-Point Boundary Value Problem of Fractional Differential Equations at Resonance

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Lei Hu ◽  
Shuqin Zhang ◽  
Ailing Shi
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Fractional Differential Equations ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Point Boundary ◽  
At Resonance ◽  
Fractional Differential

We establish the existence results for two-point boundary value problem of fractional differential equations at resonance by means of the coincidence degree theory. Furthermore, a result on the uniqueness of solution is obtained. We give an example to demonstrate our results.

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.

EXISTENCE AND GLOBAL EXPONENTIAL STABILITY OF PERIODIC SOLUTION OF A CLASS OF IMPULSIVE NETWORKS WITH INFINITE DELAYS

2007 ◽  
Vol 17 (01) ◽  
pp. 35-42 ◽  
Author(s):  
YONGHUI XIA ◽  
JINDE CAO ◽  
MUREN LIN
Keyword(s):  
Periodic Solution ◽  
Exponential Stability ◽  
Lyapunov Functions ◽  
Global Exponential Stability ◽  
Sufficient Conditions ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Mawhin’S Continuation Theorem ◽  
Neuron Networks ◽  
Infinite Delays

Sufficient conditions are obtained for the existence and global exponential stability of a unique periodic solution of a class of impulsive tow-neuron networks with variable and unbounded delays. The approaches are based on Mawhin's continuation theorem of coincidence degree theory and Lyapunov functions.

scholarly journals Multiple Positive Periodic Solutions for a Gilpin-Ayala Competition Predator-Prey System with Harvesting Terms

2012 ◽  
Vol 2012 ◽  
pp. 1-13
Author(s):  
Yongzhi Liao ◽  
Yongkun Li ◽  
Xiaoyan Dou
Keyword(s):  
Periodic Solutions ◽  
Sufficient Conditions ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Continuation Theorem ◽  
Coincidence Degree Theory ◽  
Positive Periodic Solutions ◽  
Mawhin’S Continuation Theorem ◽  
Predator Prey ◽  
Prey System

By applying Mawhin’s continuation theorem of coincidence degree theory, we study the existence of multiple positive periodic solutions for a Gilpin-Ayala competition predator-prey system with harvesting terms and obtain some sufficient conditions for the existence of multiple positive periodic solutions for the system under consideration. The result of this paper is completely new. An example is employed to illustrate our result.

scholarly journals A third-order multi-point boundary value problem at resonance with one three dimensional kernel space

2014 ◽  
Vol 30 (1) ◽  
pp. 93-100
Author(s):  
XIAOJIE LIN ◽  
◽  
BENSHENG ZHAO ◽  
ZENGJI DU ◽  
◽  
...  
Keyword(s):  
Nonlinear Differential Equations ◽  
Three Dimensional ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Existence Results ◽  
Point Boundary ◽  
Kernel Space ◽  
Third Order ◽  
At Resonance ◽  
Problem At Resonance

This paper deals with a third order nonlinear differential equations with multi-point boundary conditions. By using the coincidence degree theory, we establish some existence results of the problem at resonance under some appropriate conditions. The emphasis here is that the dimension of the linear operator is equal to three. We also give an example to demonstrate our results.

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