scholarly journals Existence and Uniqueness of Positive Solution for Third-Order Three-Point Boundary Value Problems

2014 ◽  
Vol 04 (06) ◽  
pp. 282-288
Author(s):  
Tongchun Hu ◽  
Yongping Sun
Keyword(s):  
Boundary Value Problems ◽  
Positive Solution ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Point Boundary ◽  
Third Order

scholarly journals Existence of Positive Solution to System of Nonlinear Third-Order Three-Point BVPs

2016 ◽  
Vol 2016 ◽  
pp. 1-6
Author(s):  
Jian-Ping Sun ◽  
Xue-Mei Yang ◽  
Ya-Hong Zhao
Keyword(s):  
Fixed Point ◽  
Boundary Value Problems ◽  
Positive Solution ◽  
Fixed Point Index ◽  
Boundary Value ◽  
Main Tool ◽  
Point Boundary ◽  
Point Index ◽  
Third Order

We are concerned with the following system of third-order three-point boundary value problems:u′′′(t)+f(t,v(t))=0,t∈(0,1),v′′′(t)+g(t,u(t))=0,t∈(0,1),u(0)=u′′(0)=0,u′(1)=αu(η),v(0)=v′′(0)=0, andv′(1)=αv(η), where0<η<1and0<α<1/η. By imposing some suitable conditions onfandg, we obtain the existence of at least one positive solution to the above system. The main tool used is the theory of the fixed-point index.

scholarly journals Existence and uniqueness of solutions to discrete,third-order three-point boundary value problems

Cubo (Temuco) ◽  
2021 ◽  
Vol 23 (3) ◽  
pp. 441-455
Author(s):  
Saleh S. Almuthaybiri ◽  
Jagan Mohan Jonnalagadda ◽  
Christopher C. Tisdell
Keyword(s):  
Boundary Value Problems ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Point Boundary ◽  
Uniqueness Of Solutions ◽  
Third Order

Boundary-Value Problems for Third-Order Lipschitz Ordinary Differential Equations

2014 ◽  
Vol 58 (1) ◽  
pp. 183-197 ◽  
Author(s):  
John R. Graef ◽  
Johnny Henderson ◽  
Rodrica Luca ◽  
Yu Tian
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Boundary Value Problems ◽  
Order Differential Equation ◽  
Boundary Value ◽  
Point Boundary ◽  
Third Order ◽  
Optimal Length ◽  
The Third

AbstractFor the third-order differential equationy′″ = ƒ(t, y, y′, y″), where, questions involving ‘uniqueness implies uniqueness’, ‘uniqueness implies existence’ and ‘optimal length subintervals of (a, b) on which solutions are unique’ are studied for a class of two-point boundary-value problems.

scholarly journals Solving nonlinear third-order three-point boundary value problems by boundary shape functions methods

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Ji Lin ◽  
Yuhui Zhang ◽  
Chein-Shan Liu
Keyword(s):  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Initial Conditions ◽  
Boundary Value ◽  
Accurate Solution ◽  
Point Boundary ◽  
Third Order ◽  
Boundary Shape ◽  
Free Function ◽  
New Algorithms

AbstractFor nonlinear third-order three-point boundary value problems (BVPs), we develop two algorithms to find solutions, which automatically satisfy the specified three-point boundary conditions. We construct a boundary shape function (BSF), which is designed to automatically satisfy the boundary conditions and can be employed to develop new algorithms by assigning two different roles of free function in the BSF. In the first algorithm, we let the free functions be complete functions and the BSFs be the new bases of the solution, which not only satisfy the boundary conditions automatically, but also can be used to find solution by a collocation technique. In the second algorithm, we let the BSF be the solution of the BVP and the free function be another new variable, such that we can transform the BVP to a corresponding initial value problem for the new variable, whose initial conditions are given arbitrarily and terminal values are determined by iterations; hence, we can quickly find very accurate solution of nonlinear third-order three-point BVP through a few iterations. Numerical examples confirm the performance of the new algorithms.

scholarly journals On the Solvability of Nonlinear Third-Order Two-Point Boundary Value Problems

Axioms ◽  
2020 ◽  
Vol 9 (2) ◽  
pp. 62
Author(s):  
Ravi P. Agarwal ◽  
Petio S. Kelevedjiev ◽  
Todor Z. Todorov
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Point Boundary ◽  
Third Order ◽  
Barrier Strips

Under barrier strips type assumptions we study the existence of C 3 [ 0 , 1 ] —solutions to various two-point boundary value problems for the equation x ‴ = f ( t , x , x ′ , x ″ ) . We give also some results guaranteeing positive or non-negative, monotone, convex or concave solutions.

scholarly journals Existence and Uniqueness of Solutions to Third-Order Boundary Value Problems

2021 ◽  
Vol 22 (2) ◽  
pp. 221-240
Author(s):  
S. S. Almuthaybiri ◽  
J. M. Jonnalagadda ◽  
C. C. Tisdell
Keyword(s):  
Fixed Point ◽  
Boundary Value Problems ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Uniqueness Of Solutions ◽  
Third Order ◽  
Fixed Point Methods ◽  
Bounded Sets

The purpose of this research is to connect fixed point methods with certain third-order boundary value problems in new and interesting ways. Our strategy involves an analysis of the problem under consideration within closed and bounded sets. We develop sufficient conditions under which the associated mappings will be contractive and invariant in these sets, which generates new advances concerning the existence, uniqueness and approximation of solutions.

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