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.

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 Oscillation of a functional differential equation arising from an industrial problem

1978 ◽  
Vol 26 (3) ◽  
pp. 323-329 ◽  
Author(s):  
Hiroshi Onose
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Functional Differential Equation ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Oscillatory Behavior ◽  
First Order ◽  
Functional Differential ◽  
Image Position ◽  
Industrial Problem

AbstractIn the last few years, the oscillatory behavior of functional differential equations has been investigated by many authors. But much less is known about the first-order functional differential equations. Recently, Tomaras (1975b) considered the functional differential equation and gave very interesting results on this problem, namely the sufficient conditions for its solutions to oscillate. The purpose of this paper is to extend and improve them, by examining the more general functional differential equation

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.

Nonlinear Three-Point Boundary Value Problems for a Class of Impulsive Functional Differential Equations

2009 ◽  
Vol 16 (4) ◽  
pp. 617-628
Author(s):  
Guoping Chen ◽  
Jianhua Shen
Keyword(s):  
Differential Equations ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Upper And Lower Solutions ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Lower Solution ◽  
Point Boundary ◽  
Functional Differential ◽  
Extreme Solutions

Abstract This paper is concerned with the existence of extreme solutions of nonlinear three-point boundary value problems for a class of first order impulsive functional differential equations. In the presence of a lower solution α and an upper solution β with the classical condition α ≤ β or the reversed ordering condition β ≤ α, some sufficient conditions for the existence of extreme solutions are obtained by using the method of upper and lower solutions coupled with the monotone iterative technique.

scholarly journals A Class of Coupled Causal Differential Equations

Symmetry ◽  
2018 ◽  
Vol 10 (10) ◽  
pp. 421 ◽  
Author(s):  
Wen-Li Wang ◽  
Jing-Feng Tian ◽  
Wing-Sum Cheung
Keyword(s):  
Differential Equations ◽  
Sufficient Conditions ◽  
Monotone Iterative Technique ◽  
Comparison Theorems ◽  
Iterative Technique ◽  
Monotone Iterative ◽  
Extreme Solutions

In this thesis, we consider the existence of extreme solutions to a class of coupled causal differential equations. By utilizing two comparison theorems and a monotone iterative technique, we have obtained sufficient conditions under which the equations have extreme solutions. One practical example is presented.

scholarly journals Existence and iteration of positive solution for fractional integral boundary value problems with p-Laplacian operator

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Ying He ◽  
Bo Bi
Keyword(s):  
Boundary Value ◽  
Upper And Lower Solutions ◽  
Sufficient Conditions ◽  
Monotone Iterative Technique ◽  
Laplacian Operator ◽  
Integral Boundary ◽  
Monotone Iterative ◽  
Fractional Differential ◽  
Integral Boundary Value Problems ◽  
The Given

Abstract This paper is concerned with an integral boundary value problem of fractional differential equations with p-Laplacian operator. Sufficient conditions ensuring the existence of extremal solutions for the given problem are obtained. Our results are based on the method of upper and lower solutions and monotone iterative technique.

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