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.

Method of upper and lower solutions for coupled system of nonlinear fractional integro-differential equations with advanced arguments

2017 ◽  
Vol 67 (1) ◽  
pp. 89-98
Author(s):  
Neda Khodabakhshi ◽  
S. Mansour Vaezpour ◽  
J. Juan Trujillo
Keyword(s):  
Differential Equations ◽  
Iterative Method ◽  
Upper And Lower Solutions ◽  
Coupled System ◽  
Extremal Solutions ◽  
Monotone Iterative Method ◽  
Monotone Iterative

AbstractIn this paper, by means of upper and lower solutions, we develop monotone iterative method for the existence of extremal solutions for coupled system of nonlinear fractional integro-differential equations with advanced arguments. We illustrate this technique with the help of an example.

scholarly journals Iterative Approximation of the Minimal and Maximal Positive Solutions for Multipoint Fractional Boundary Value Problem on an Unbounded Domain

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
Guotao Wang ◽  
Sanyang Liu ◽  
Lihong Zhang
Keyword(s):  
Iterative Method ◽  
Boundary Value Problem ◽  
Positive Solutions ◽  
Unbounded Domain ◽  
Boundary Value ◽  
Monotone Iterative Method ◽  
Fractional Boundary Value Problem ◽  
Iterative Approximation ◽  
Monotone Iterative

By employing the monotone iterative method, this paper not only establishes the existence of the minimal and maximal positive solutions for multipoint fractional boundary value problem on an unbounded domain, but also develops two computable explicit monotone iterative sequences for approximating the two positive solutions. An example is given for the illustration of the main result.

Sign in / Sign up

Export Citation Format

Share Document