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 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 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 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.

scholarly journals Higher Order Nonlocal Boundary Value Problems at Resonance on the Half-line

2020 ◽  
Vol 13 (1) ◽  
pp. 33-47
Author(s):  
Samuel Iyase ◽  
Abiodun Opanuga
Keyword(s):  
Boundary Value Problems ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Higher Order ◽  
Half Line ◽  
Index Zero ◽  
Nonlocal Boundary Value Problems ◽  
At Resonance ◽  
Fredholm Map

This paper investigates the solvability of a class of higher order nonlocal boundaryvalue problems of the formu(n)(t) = g(t, u(t), u0(t)· · · u(n−1)(t)), a.e. t ∈ (0, ∞)subject to the boundary conditionsu(n−1)(0) = (n − 1)!ξn−1u(ξ), u(i)(0) = 0, i = 1, 2, . . . , n − 2,u(n−1)(∞) = Z ξ0u(n−1)(s)dA(s)where ξ > 0, g : [0, ∞) × <n −→ < is a Caratheodory’s function,A : [0, ξ] −→ [0, 1) is a non-decreasing function with A(0) = 0, A(ξ) = 1. The differential operatoris a Fredholm map of index zero and non-invertible. We shall employ coicidence degree argumentsand construct suitable operators to establish existence of solutions for the above higher ordernonlocal boundary value problems at resonance.

scholarly journals Solvability of integral boundary value problems at resonance in $R^{n}$

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Shiying Song ◽  
Shuman Meng ◽  
Yujun Cui
Keyword(s):  
Differential Equation ◽  
Boundary Value Problems ◽  
Resonance Condition ◽  
Boundary Value ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Integral Boundary ◽  
At Resonance ◽  
Matrix Diagonalization ◽  
Integral Boundary Value Problems

Abstract Under a resonance condition involving integral boundary value problems for a second-order nonlinear differential equation in $\mathbb{R}^{n}$ R n , we show its solvability by using the coincidence degree theory of Mawhin and the theory of matrix diagonalization in linear algebra.

System of nonlocal resonant boundary value problems involving p-Laplacian

2018 ◽  
Vol 68 (4) ◽  
pp. 837-844
Author(s):  
Katarzyna Szymańska-Dębowska
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Bounded Variation ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Function Of Bounded Variation ◽  
One Dimensional ◽  
The One

Abstract Our aim is to study the existence of solutions for the following system of nonlocal resonant boundary value problem $$\begin{array}{} \displaystyle (\varphi (x'))' =f(t,x,x'),\quad x'(0)=0, \quad x(1)=\int\limits_{0 }^{1}x(s){\rm d} g(s), \end{array}$$ where the function ϕ : ℝn → ℝn is given by ϕ (s) = (φp1(s1), …, φpn(sn)), s ∈ ℝn, pi > 1 and φpi : ℝ → ℝ is the one dimensional pi -Laplacian, i = 1,…,n, f : [0,1] × ℝn × ℝn → ℝn is continuous and g : [0,1] → ℝn is a function of bounded variation. The proof of the main result is depend upon the coincidence degree theory.

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 Existence of Solutions to the Boundary Value Problems for a Class of P-Laplacian Equations at Resonance

2016 ◽  
Vol 8 (3) ◽  
pp. 37
Author(s):  
Lina Zhou ◽  
Weihua Jiang
Keyword(s):  
Boundary Value Problems ◽  
Banach Spaces ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
At Resonance ◽  
Laplacian Equations

By the generalizing the extension of the continuous theorem of Ge and Ren and constructing suitable Banach spaces and operators, we investigate the existence-solutions to the boundary value problems for a class of  p-Laplacian equations. Finally an example is given to illustrate our results.

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