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.

A Note on the Uniqueness of Positive Solutions for Singular Boundary Value Problems

2011 ◽  
Vol 2 (3) ◽  
pp. 43-50
Author(s):  
Fu-Hsiang Wong ◽  
Sheng-Ping Wang ◽  
Hsiang-Feng Hong
Keyword(s):  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Positive Solution ◽  
Positive Solutions ◽  
Boundary Value ◽  
Uniqueness Theorems ◽  
Singular Boundary ◽  
Sufficient Condition ◽  
Singular Boundary Value Problems

In this paper, the authors examine sufficient condition for the uniqueness of positive solutions of singular Strum-Liouville boundary value problems. The authors use the uniqueness theorems of (E) with respect to the boundary conditions to show that the boundary value problems have one positive solution.

scholarly journals Positive solutions of fourth-order superlinear singular boundary value problems

2002 ◽  
Vol 66 (1) ◽  
pp. 95-104 ◽  
Author(s):  
Guoliang Shi ◽  
Shaozhu Chen
Keyword(s):  
Boundary Value Problems ◽  
Positive Solutions ◽  
Fourth Order ◽  
Closed Interval ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Singular Boundary ◽  
Point Boundary ◽  
Singular Boundary Value Problems ◽  
Necessary And Sufficient

This paper investigates fourth-order superlinear singular two-point boundary value problems and obtains necessary and sufficient conditions for existence of C2 or C3 positive solutions on the closed interval.

scholarly journals A Galerkin method ofO(h2)for singular boundary value problems

2002 ◽  
Vol 29 (6) ◽  
pp. 361-369
Author(s):  
G. K. Beg ◽  
M. A. El-Gebeily
Keyword(s):  
Galerkin Method ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Basis Functions ◽  
Singular Boundary ◽  
Point Boundary ◽  
Singular Boundary Value Problems ◽  
Special Basis

We describe a Galerkin method with special basis functions for a class of singular two-point boundary value problems. The convergence is shown which is ofO(h2)for a certain subclass of the problems.

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