Extremal solutions of a boundary value problem for a sixth-order equation

2014 ◽  
Vol 50 (2) ◽  
pp. 141-146
Author(s):  
M. M. Adjustovs ◽  
A. J. Lepins
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value ◽  
Order Equation ◽  
Sixth Order ◽  
Extremal Solutions

scholarly journals Multiple Solutions for a Sixth Order Boundary Value Problem

2021 ◽  
Vol 22 (1) ◽  
pp. 1-12
Author(s):  
A. L. M. Martinez ◽  
C. A. Pendeza Martinez ◽  
G. M. Bressan ◽  
R. M. Souza ◽  
E. W. Stiegelmeier
Keyword(s):  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Numerical Method ◽  
Multiple Solutions ◽  
Boundary Value ◽  
Order Equation ◽  
Sixth Order ◽  
Contraction Principle ◽  
Banach’S Contraction Principle

This work presents conditions for the existence of multiple solutions for a sixth order equation with homogeneous boundary conditions using Avery Peterson's theorem. In addition, non-trivial examples are presented and a new numerical method based on the Banach's Contraction Principle is introduced.  

scholarly journals A monotone iterative method for boundary value problems of parametric differential equations

2001 ◽  
Vol 14 (2) ◽  
pp. 183-187 ◽  
Author(s):  
Xinzhi Liu ◽  
Farzana A. McRae
Keyword(s):  
Differential Equations ◽  
Iterative Method ◽  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Upper And Lower Solutions ◽  
Extremal Solutions ◽  
Monotone Iterative Method ◽  
Monotone Iterative ◽  
Monotone Sequences

This paper studies boundary value problems for parametric differential equations. By using the method of upper and lower solutions, monotone sequences are constructed and proved to converge to the extremal solutions of the boundary value problem.

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