Monotone iterative technique for functional differential equations with retardation and anticipation

2007 ◽  
Vol 66 (10) ◽  
pp. 2237-2242 ◽  
Author(s):  
T. Gnana Bhaskar ◽  
V. Lakshmikantham ◽  
J. Vasundhara Devi
Keyword(s):  
Differential Equations ◽  
Functional Differential Equations ◽  
Monotone Iterative Technique ◽  
Iterative Technique ◽  
Monotone Iterative ◽  
Functional Differential

A class of fractional impulsive functional differential equations with nonlocal conditions

2016 ◽  
Vol 66 (4) ◽  
Author(s):  
Yiliang Liu ◽  
Jiangfeng Han
Keyword(s):  
Differential Equations ◽  
Comparison Theorem ◽  
Existence Of Solutions ◽  
Functional Differential Equations ◽  
Nonlocal Conditions ◽  
Monotone Iterative Technique ◽  
Extremal Solutions ◽  
Iterative Technique ◽  
Monotone Iterative ◽  
Functional Differential

AbstractIn this paper, we deal with the existence of solutions for the fractional impulsive functional differential equations with nonlocal conditions. Then we build a new comparison theorem and obtain the existence of extremal solutions and quasi-solutions by use of the monotone iterative technique and the method of lower and upper solutions.

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.

scholarly journals Integral BVPs for a Class of First-Order Impulsive Functional Differential Equations

2010 ◽  
Vol 2010 ◽  
pp. 1-11 ◽  
Author(s):  
Xiaofei He ◽  
Jingli Xie ◽  
Guoping Chen ◽  
Jianhua Shen
Keyword(s):  
Differential Equations ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Monotone Iterative Technique ◽  
Integral Boundary ◽  
First Order ◽  
Monotone Iterative ◽  
Functional Differential ◽  
Integral Boundary Value Problems ◽  
Extreme Solutions

The methods of lower and upper solutions and monotone iterative technique are employed to the study of integral boundary value problems for a class of first-order impulsive functional differential equations. Sufficient conditions are obtained for the existence of extreme solutions.

Ordinary Differential Equations with Nonlinear Boundary Conditions

2002 ◽  
Vol 9 (2) ◽  
pp. 287-294
Author(s):  
Tadeusz Jankowski
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Ordinary Differential Equations ◽  
Nonlinear Boundary ◽  
Nonlinear Boundary Conditions ◽  
Existence Results ◽  
Monotone Iterative Technique ◽  
Lower And Upper Solutions ◽  
Iterative Technique ◽  
Monotone Iterative

Abstract The method of lower and upper solutions combined with the monotone iterative technique is used for ordinary differential equations with nonlinear boundary conditions. Some existence results are formulated for such problems.

Sign in / Sign up

Export Citation Format

Share Document