scholarly journals On the Solvability of a Resonant Third-Order Integral m-Point Boundary Value Problem on the Half-Line

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
O. F. Imaga ◽  
J. G. Oghonyon ◽  
P. O. Ogunniyi
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Existence Results ◽  
Coincidence Degree Theory ◽  
Half Line ◽  
Point Boundary ◽  
Third Order ◽  
At Resonance

In this work, the existence of at least one solution for the following third-order integral and m -point boundary value problem on the half-line at resonance ρ t u ′ t ″ = w t , u t , u ′ t , u ″ t , t ∈ 0 , ∞ , u 0 = ∑ j = 1 m   α j ∫ 0 η j   u t d t , u ′ 0 = 0 , lim t ⟶ ∞ ρ t u ′ t ′ = 0 , will be investigated. The Mawhin’s coincidence degree theory will be used to obtain existence results while an example will be used to validate the result obatined.

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.

scholarly journals On a class of second-order impulsive boundary value problem at resonance

2006 ◽  
Vol 2006 ◽  
pp. 1-11
Author(s):  
Guolan Cai ◽  
Zengji Du ◽  
Weigao Ge
Keyword(s):  
Boundary Value Problem ◽  
Existence Result ◽  
Boundary Value ◽  
General Theorem ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Point Boundary ◽  
At Resonance ◽  
Impulsive Boundary Value Problem ◽  
Problem At Resonance

We consider the following impulsive boundary value problem,x″(t)=f(t,x,x′),t∈J\{t1,t2,…,tk},Δx(ti)=Ii(x(ti),x′(ti)),Δx′(ti)=Ji(x(ti),x′(ti)),i=1,2,…,k,x(0)=(0),x′(1)=∑j=1m−2αjx′(ηj). By using the coincidence degree theory, a general theorem concerning the problem is given. Moreover, we get a concrete existence result which can be applied more conveniently than recent results. Our results extend some work concerning the usualm-point boundary value problem at resonance without impulses.

scholarly journals Solvability of a Third-Order Multipoint Boundary Value Problem at Resonance

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Zengji Du ◽  
Bensheng Zhao ◽  
Zhanbing Bai
Keyword(s):  
Boundary Value Problem ◽  
Existence Result ◽  
Boundary Value ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Third Order ◽  
Multipoint Boundary ◽  
At Resonance ◽  
Problem At Resonance ◽  
Multipoint Boundary Value Problem

We discuss a third-order multipoint boundary value problem under some appropriate resonance conditions. By using the coincidence degree theory, we establish the existence result of solutions. The emphasis here is that the dimension of the linear operator is equal to two. Our results supplement other results.

scholarly journals On the Existence of Coupled Fractional Jerk Equations with Multi-Point Boundary Conditions

Axioms ◽  
2021 ◽  
Vol 10 (2) ◽  
pp. 103
Author(s):  
Lei Hu ◽  
Yaozhen Han ◽  
Shuqin Zhang
Keyword(s):  
Boundary Conditions ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Existence Of Solution ◽  
Existence Results ◽  
Coincidence Degree Theory ◽  
Point Boundary ◽  
First Time

By coincidence degree theory due to Mawhin, some sufficient conditions for the existence of solution for a class of coupled jerk equations with multi-point conditions are established. The new existence results have not yet been reported before. Novel coupled fractional jerk equations with resonant boundary value conditions are discussed in detail for the first time. Our work is interesting and complements known 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 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 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 a fractional-order p-Laplacian boundary value problem at resonance on the half-line with two dimensional kernel

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
O. F. Imaga ◽  
S. A. Iyase
Keyword(s):  
Differential Operator ◽  
Boundary Value Problem ◽  
Fractional Order ◽  
Boundary Value ◽  
Coincidence Degree ◽  
Half Line ◽  
At Resonance ◽  
Fractional Differential Operator ◽  
Fractional Differential ◽  
Problem At Resonance

AbstractIn this work, we consider the solvability of a fractional-order p-Laplacian boundary value problem on the half-line where the fractional differential operator is nonlinear and has a kernel dimension equal to two. Due to the nonlinearity of the fractional differential operator, the Ge and Ren extension of Mawhin’s coincidence degree theory is applied to obtain existence results for the boundary value problem at resonance. Two examples are used to validate the established results.

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