A multipoint Birkhoff type boundary value problem

2015 ◽  
Vol 23 (1) ◽  
pp. 1-11 ◽  
Author(s):  
Francesco A. Costabile ◽  
Anna Napoli
Keyword(s):  
Boundary Value Problem ◽  
Numerical Solution ◽  
Collocation Method ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Uniqueness Of Solution ◽  
Multipoint Boundary ◽  
Type Boundary ◽  
Theoretical Results ◽  
Multipoint Boundary Value Problem

AbstractA multipoint boundary value problem is considered. The existence and uniqueness of solution is proved. Then, for the numerical solution, a general collocation method is proposed.Numerical experiments confirm theoretical results.

scholarly journals Lidstone–Euler Second-Type Boundary Value Problems: Theoretical and Computational Tools

2021 ◽  
Vol 18 (5) ◽  
Author(s):  
Francesco Aldo Costabile ◽  
Maria Italia Gualtieri ◽  
Anna Napoli
Keyword(s):  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Existence And Uniqueness ◽  
Interpolation Problem ◽  
Boundary Value ◽  
Computational Tools ◽  
Numerical Examples ◽  
Odd Order ◽  
Uniqueness Of The Solution ◽  
Type Boundary

AbstractGeneral nonlinear high odd-order differential equations with Lidstone–Euler boundary conditions of second type are treated both theoretically and computationally. First, the associated interpolation problem is considered. Then, a theorem of existence and uniqueness of the solution to the Lidstone–Euler second-type boundary value problem is given. Finally, for a numerical solution, two different approaches are illustrated and some numerical examples are included to demonstrate the validity and applicability of the proposed algorithms.

scholarly journals Positive Solutions for Resonant and Nonresonant Nonlinear Third-Order Multipoint Boundary Value Problems

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Liu Yang ◽  
Chunfang Shen ◽  
Dapeng Xie
Keyword(s):  
Boundary Value Problem ◽  
Positive Solution ◽  
Positive Solutions ◽  
Boundary Value ◽  
Type Theorem ◽  
Third Order ◽  
Multipoint Boundary ◽  
Multipoint Boundary Value Problems ◽  
First Time ◽  
Multipoint Boundary Value Problem

Positive solutions for a kind of third-order multipoint boundary value problem under the nonresonant conditions and the resonant conditions are considered. In the nonresonant case, by using the Leggett-Williams fixed point theorem, the existence of at least three positive solutions is obtained. In the resonant case, by using the Leggett-Williams norm-type theorem due to O’Regan and Zima, the existence result of at least one positive solution is established. It is remarkable to point out that it is the first time that the positive solution is considered for the third-order boundary value problem at resonance. Some examples are given to demonstrate the main results of the paper.

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