scholarly journals Existence and Uniqueness of Solution to Nonlinear Boundary Value Problems with Sign-Changing Green’s Function

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Peiguo Zhang ◽  
Lishan Liu ◽  
Yonghong Wu
Keyword(s):  
Green’S Function ◽  
Boundary Value Problems ◽  
Green's Function ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Contraction Mapping Principle ◽  
Nonlinear Boundary Value Problems ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Equation Boundary

By using the cone theory and the Banach contraction mapping principle, the existence and uniqueness results are established for nonlinear higher-order differential equation boundary value problems with sign-changing Green’s function. The theorems obtained are very general and complement previous known results.

scholarly journals GREEN’S FUNCTION AND EXISTENCE OF SOLUTIONS FOR A THIRD-ORDER THREE-POINT BOUNDARY VALUE PROBLEM

2019 ◽  
Vol 24 (2) ◽  
pp. 171-178 ◽  
Author(s):  
Sergey Smirnov
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Point Boundary ◽  
Nonlinear Boundary Value Problems ◽  
Uniqueness Of Solutions ◽  
Third Order ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results

The solutions of third-order three-point boundary value problemx′′′+f(t,x) = 0, t∈[a,b],x(a) =x′(a) = 0, x(b) =kx(η),whereη∈(a,b),k∈R,f∈C([a,b]×R,R) andf(t,0)6= 0, are the subject of thisinvestigation. In order to establish existence and uniqueness results for the solutions,attention is focused on applications of the corresponding Green’s function. As anapplication, also one example is given to illustrate the result.Keywords:Green’s function, nonlinear boundary value problems, three-point boundaryconditions, existence and uniqueness of solutions.

scholarly journals Noninstantaneous Impulsive Fractional Quantum Hahn Integro-Difference Boundary Value Problems

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 671 ◽  
Author(s):  
Surang Sitho ◽  
Chayapat Sudprasert ◽  
Sotiris K. Ntouyas ◽  
Jessada Tariboon
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Integral Boundary Conditions ◽  
Contraction Mapping Principle ◽  
Integral Boundary ◽  
Fractional Quantum ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Nonlinear Alternative ◽  
Banach Contraction

In this paper, we study the existence and uniqueness results for noninstantaneous impulsive fractional quantum Hahn integro-difference boundary value problems with integral boundary conditions, by using Banach contraction mapping principle and Leray–Schauder nonlinear alternative. Examples are included illustrating the obtained results. To the best of our knowledge, no work has reported on the existence of solutions to the Hahn-difference equation with noninstantaneous impulses.

scholarly journals SHARPER EXISTENCE AND UNIQUENESS RESULTS FOR SOLUTIONS TO THIRD-ORDER BOUNDARY VALUE PROBLEMS

2020 ◽  
Vol 25 (3) ◽  
pp. 409-420 ◽  
Author(s):  
Saleh S. Almuthaybiri ◽  
Christopher C. Tisdell
Keyword(s):  
Boundary Value Problems ◽  
Existence And Uniqueness ◽  
Contraction Mapping ◽  
Boundary Value ◽  
Uniqueness Of Solutions ◽  
Third Order ◽  
Contraction Mapping Theorem ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Banach’S Fixed Point Theorem

The purpose of this note is to sharpen Smirnov’s recent work on existence and uniqueness of solutions to third-order ordinary differential equations that are subjected to two- and three-point boundary conditions. The advancement is achieved in the following ways. Firstly, we provide sharp and sharpened estimates for integrals regarding various Green’s functions. Secondly, we apply these sharper estimates to problems in conjunction with Banach’s fixed point theorem. Thirdly, we apply Rus’s contraction mapping theorem in a metric space, where two metrics are employed. Our new results improve those of Smirnov by showing that a larger class of boundary value problems admit a unique solution.

scholarly journals A Study of Caputo-Hadamard-Type Fractional Differential Equations with Nonlocal Boundary Conditions

2016 ◽  
Vol 2016 ◽  
pp. 1-9 ◽  
Author(s):  
Wafa Shammakh
Keyword(s):  
Differential Equations ◽  
Green’S Function ◽  
Green's Function ◽  
Fractional Differential Equations ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Conditions ◽  
Nonlinear Boundary Value Problems ◽  
Uniqueness Results ◽  
Fractional Differential

Existence and uniqueness results of positive solutions to nonlinear boundary value problems for Caputo-Hadamard fractional differential equations by using some fixed point theorems are presented. The related Green’s function for the boundary value problem is given, and some useful properties of Green’s function are obtained. Example is presented to illustrate the main results.

scholarly journals Notes on Local and Nonlocal Intuitionistic Fuzzy Fractional Boundary Value Problems with Caputo Fractional Derivatives

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Ali El Mfadel ◽  
Said Melliani ◽  
M’hamed Elomari
Keyword(s):  
Boundary Value Problems ◽  
Existence And Uniqueness ◽  
Fractional Derivatives ◽  
Fixed Point Theorems ◽  
Boundary Value ◽  
Caputo Fractional Derivatives ◽  
Existence And Uniqueness Results ◽  
Intuitionistic Fuzzy ◽  
Uniqueness Results ◽  
Fractional Boundary Value Problems

In this paper, we investigate the existence and uniqueness results of intuitionistic fuzzy local and nonlocal fractional boundary value problems by employing intuitionistic fuzzy fractional calculus and some fixed-point theorems. As an application, we conclude this manuscript by giving an example to illustrate the obtained results.

scholarly journals Existence and Uniqueness Results for a Class of Singular Fractional Boundary Value Problems with the p-Laplacian Operator via the Upper and Lower Solutions Approach

2020 ◽  
Vol 2020 ◽  
pp. 1-15
Author(s):  
KumSong Jong ◽  
HuiChol Choi ◽  
KyongJun Jang ◽  
SunAe Pak
Keyword(s):  
Fixed Point ◽  
Boundary Value Problems ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Upper And Lower Solutions ◽  
Gauss Hypergeometric Function ◽  
Laplacian Operator ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Nonlinear Alternative

In this paper, we study the existence and uniqueness of positive solutions to a class of multipoint boundary value problems for singular fractional differential equations with the p-Laplacian operator. Here, the nonlinear source term f permits singularity with respect to its time variable t. Some fixed-point theorems such as the Leray-Schauder nonlinear alternative, the Schauder fixed-point theorem, and the Banach contraction mapping principle and the properties of the Gauss hypergeometric function are used to prove our main results. And by employing the upper and lower solutions technique, we derive a new approach to obtain the maximal and minimal solutions to the given problem. Finally, we present some examples to demonstrate our existence and uniqueness results.

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