scholarly journals New Modified Adomin Decomp osition Metho d for Boundary Value Problems of Higher-order Ordinary Differential Equation

2020 ◽  
pp. 20-37
Author(s):  
Zainab Ali Ab du Al-Rabahi ◽  
Yahya Qaid Hasan
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Differential Operator ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Inverse Operator ◽  
Higher Order ◽  
Third Order ◽  
Order Ordinary Differential Equation ◽  
Solving Equations

This study will present a new modified differential operator for solving third-order boundary value problems into higher-order ordinary differential equation. We found the differential operator for new three inverse operator which can be applied for solving equations at more than one type in different conditions. We put a detailed plan for five non-linear examples from a high-order, we get dynamic and quickly to the exact solution.

scholarly journals On the third order boundary value problems with asymmetric nonlinearity

2011 ◽  
Vol 16 (2) ◽  
pp. 231-241 ◽  
Author(s):  
Sergey Smirnov
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Third Order ◽  
Number Of Solutions ◽  
The Third ◽  
Asymmetric Nonlinearity ◽  
Autonomous Ordinary Differential Equation

The author considers two point third order boundary value problem with asymmetric nonlinearity. The structure and oscillatory properties of solutions of the third order nonlinear autonomous ordinary differential equation are discussed. Results on the estimation of the number of solutions to boundary value problem are provided. An illustrative example is given.

scholarly journals The Existence of Positive Solutions for a Nonlinear Sixth-Order Boundary Value Problem

2012 ◽  
Vol 2012 ◽  
pp. 1-12
Author(s):  
Wanjun Li ◽  
Liyuan Zhang ◽  
Yukun An
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Boundary Value ◽  
Sixth Order ◽  
Order Ordinary Differential Equation ◽  
Existence Of Positive Solutions ◽  
Bifurcation Methods

By using the Krein-Rutman theorem and bifurcation methods, we discuss the existence of positive solutions for the boundary value problems of a sixth-order ordinary differential equation.

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.

EXISTENCE THEOREMS OF POSITIVE SOLUTIONS FOR FOURTH-ORDER FOUR-POINT BOUNDARY VALUE PROBLEMS

2004 ◽  
Vol 02 (01) ◽  
pp. 71-85 ◽  
Author(s):  
YUJI LIU ◽  
WEIGAO GE
Keyword(s):  
Differential Equation ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Fourth Order ◽  
Existence Theorems ◽  
Boundary Value ◽  
Growth Conditions ◽  
Point Boundary ◽  
Order Ordinary Differential Equation ◽  
Order Four

In this paper, we study four-point boundary value problems for a fourth-order ordinary differential equation of the form [Formula: see text] with one of the following boundary conditions: [Formula: see text] or [Formula: see text] Growth conditions on f which guarantee existence of at least three positive solutions for the problems (E)–(B1) and (E)–(B2) are imposed.

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