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 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 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 results for a second order nonlocal boundary value problem at resonance

2016 ◽  
Vol 53 (1) ◽  
pp. 42-52
Author(s):  
Katarzyna Szymańska-Dȩbowska
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Existence Results ◽  
Function Of Bounded Variation ◽  
Nonlocal Boundary Value Problem ◽  
At Resonance ◽  
Problem At Resonance

The paper focuses on existence of solutions of a system of nonlocal resonant boundary value problems , where f : [0, 1] × ℝk → ℝk is continuous and g : [0, 1] → ℝk is a function of bounded variation. Imposing on the function f the following condition: the limit limλ→∞f(t, λ a) exists uniformly in a ∈ Sk−1, we have shown that the problem has at least one solution.

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 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.

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