scholarly journals Positive Solutions for a Class of Singular Boundary Value Problems with Fractionalq-Difference Equations

2015 ◽  
Vol 2015 ◽  
pp. 1-8
Author(s):  
Jufang Wang ◽  
Changlong Yu ◽  
Yanping Guo
Keyword(s):  
Boundary Value Problems ◽  
Difference Equations ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Partially Ordered Sets ◽  
Singular Boundary ◽  
Singular Boundary Value Problems ◽  
Ordered Sets ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results

We discuss a class of singular boundary value problems of fractionalq-difference equations. Some existence and uniqueness results are obtained by a fixed point theorem in partially ordered sets. Finally, we give an example to illustrate the results.

scholarly journals New Results for Multipoint Singular Boundary Value Problems on a Measure Chain

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Yan Sun ◽  
Yongping Sun ◽  
Patricia J. Y. Wong
Keyword(s):  
Boundary Value Problems ◽  
Positive Solutions ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Singular Boundary ◽  
Sufficient Condition ◽  
Point Boundary ◽  
Singular Boundary Value Problems ◽  
Second Order Differential Equations ◽  
Maximal Principle

We study the existence and uniqueness of positive solutions for a class of singularm-point boundary value problems of second order differential equations on a measure chain. A sharper sufficient condition for the existence and uniqueness ofCrd⁡1[0,T]positive solutions as well asCrd⁡1[0,T]positive solutions is obtained by the technique of lower and upper solutions and the maximal principle theorem.

Higher-order singular multi-point boundary-value problems on time scales

2011 ◽  
Vol 54 (2) ◽  
pp. 345-361 ◽  
Author(s):  
Abdulkadir Dogan ◽  
John R. Graef ◽  
Lingju Kong
Keyword(s):  
Boundary Value Problems ◽  
Positive Solutions ◽  
Operator Theory ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Higher Order ◽  
Singular Boundary ◽  
Singular Boundary Value Problems ◽  
Mixed Monotone Operator ◽  
Monotone Operator Theory

AbstractWe study classes of higher-order singular boundary-value problems on a time scale $\mathbb{T}$ with a positive parameter λ in the differential equations. A homeomorphism and homomorphism ø are involved both in the differential equation and in the boundary conditions. Criteria are obtained for the existence and uniqueness of positive solutions. The dependence of positive solutions on the parameter λ is studied. Applications of our results to special problems are also discussed. Our analysis mainly relies on the mixed monotone operator theory. The results here are new, even in the cases of second-order differential and difference equations.

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 Nonlocal Boundary Value Problems forq-Difference Equations and Inclusions

2015 ◽  
Vol 2015 ◽  
pp. 1-12
Author(s):  
Sotiris K. Ntouyas ◽  
Jessada Tariboon
Keyword(s):  
Boundary Value Problems ◽  
Difference Equations ◽  
Fixed Point Theorems ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Integral Boundary Conditions ◽  
Integral Boundary ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Quantum Numbers

We study boundary value problems forq-difference equations and inclusions with nonlocal and integral boundary conditions which have different quantum numbers. Some new existence and uniqueness results are obtained by using fixed point theorems. Examples are given to illustrate the results.

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