Monotone iterative method for functional differential equations

1998 ◽  
Vol 32 (6) ◽  
pp. 741-747 ◽  
Author(s):  
Juan J. Nieto ◽  
Yu Jiang ◽  
Yan Jurang
Keyword(s):  
Differential Equations ◽  
Iterative Method ◽  
Functional Differential Equations ◽  
Monotone Iterative Method ◽  
Monotone Iterative ◽  
Functional Differential

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 MultiPoint BVPs for Second-Order Functional Differential Equations with Impulses

2009 ◽  
Vol 2009 ◽  
pp. 1-16
Author(s):  
Xuxin Yang ◽  
Zhimin He ◽  
Jianhua Shen
Keyword(s):  
Differential Equations ◽  
Upper And Lower Solutions ◽  
Functional Differential Equations ◽  
Existence Results ◽  
Monotone Iterative Technique ◽  
Second Order ◽  
Monotone Iterative ◽  
Functional Differential ◽  
Extreme Solutions ◽  
Multipoint Boundary Value Problem

This paper is concerned about the existence of extreme solutions of multipoint boundary value problem for a class of second-order impulsive functional differential equations. We introduce a new concept of lower and upper solutions. Then, by using the method of upper and lower solutions introduced and monotone iterative technique, we obtain the existence results of extreme solutions.

Monotone iterative method for a class of nonlinear fractional differential equations

2012 ◽  
Vol 15 (2) ◽  
Author(s):  
Guotao Wang ◽  
Dumitru Baleanu ◽  
Lihong Zhang
Keyword(s):  
Differential Equations ◽  
Iterative Method ◽  
Fractional Differential Equations ◽  
Monotone Iterative Technique ◽  
Monotone Iterative Method ◽  
Iterative Technique ◽  
Nonlinear Fractional Differential Equations ◽  
Monotone Iterative ◽  
Liouville Fractional Derivative ◽  
Fractional Differential

AbstractBy applying the monotone iterative technique and the method of lower and upper solutions, this paper investigates the existence of extremal solutions for a class of nonlinear fractional differential equations, which involve the Riemann-Liouville fractional derivative D q x(t). A new comparison theorem is also build. At last, an example is given to illustrate our main results.

An iterative method for functional differential equations

2005 ◽  
Vol 161 (1) ◽  
pp. 265-269 ◽  
Author(s):  
Mustapha Yebdri ◽  
Sidi Mohammed Bouguima ◽  
Ovide Arino
Keyword(s):  
Differential Equations ◽  
Iterative Method ◽  
Functional Differential Equations ◽  
Functional Differential
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