Monotone-iterative method for mixed boundary value problems for generalized difference equations with “maxima”

2013 ◽  
Vol 43 (1-2) ◽  
pp. 213-233 ◽  
Author(s):  
Ravi P. Agarwal ◽  
S. Hristova ◽  
A. Golev ◽  
K. Stefanova
Keyword(s):  
Iterative Method ◽  
Boundary Value Problems ◽  
Difference Equations ◽  
Mixed Boundary ◽  
Boundary Value ◽  
Monotone Iterative Method ◽  
Mixed Boundary Value Problems ◽  
Monotone Iterative

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.

scholarly journals Monotone Iterative Method for Two Types of Integral Boundary Value Problems of a Nonlinear Fractional Differential System with Deviating Arguments

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Jungang Chen ◽  
Xi Qin
Keyword(s):  
Iterative Method ◽  
Boundary Value Problems ◽  
Differential System ◽  
Boundary Value ◽  
Monotone Iterative Method ◽  
Integral Boundary ◽  
Monotone Iterative ◽  
Fractional Differential System ◽  
Fractional Differential ◽  
Integral Boundary Value Problems

This paper concerns on two types of integral boundary value problems of a nonlinear fractional differential system, i . e ., nonlocal strip integral boundary value problems and coupled integral boundary value problems. With the aid of the monotone iterative method combined with the upper and lower solutions, the existence of extremal system of solutions for the above two types of differential systems is investigated. In addition, a new comparison theorem for fractional differential system is also established, which is crucial for the proof of the main theorem of this paper. At the end, an example explaining how our studies can be used is also given.

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