Projection method for discretization of boundary-value problems for a fourth-order ordinary differential equation

1994 ◽  
Vol 69 (6) ◽  
pp. 1379-1384
Author(s):  
A. A. Klunnik ◽  
V. G. Prikazchikov
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Boundary Value Problems ◽  
Projection Method ◽  
Fourth Order ◽  
Boundary Value ◽  
Order Ordinary Differential Equation

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.

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.

Existence of Solutions for Fourth Order Nonlocal Boundary Value Problems

2006 ◽  
Vol 13 (3) ◽  
pp. 473-484
Author(s):  
Johnny Henderson ◽  
Ding Ma
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Fourth Order ◽  
Existence Of Solutions ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Conditions ◽  
Existence Results ◽  
Order Ordinary Differential Equation

Abstract Uniqueness implies existence results are obtained for solutions of the fourth order ordinary differential equation, 𝑦(4) = 𝑓(𝑥, 𝑦, 𝑦′, 𝑦″, 𝑦‴), satisfying 5-point, 4-point and 3-point nonlocal boundary conditions.

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