Monotone Iterative Techniques and a Periodic Boundary Value Problem for First Order Differential Equations with a Functional Argument

2000 ◽  
Vol 7 (2) ◽  
pp. 373-378
Author(s):  
Aiqin Qi ◽  
Yansheng Liu
Keyword(s):  
Differential Equations ◽  
Periodic Boundary ◽  
Boundary Value ◽  
Upper And Lower Solutions ◽  
Initial Value ◽  
First Order ◽  
Monotone Iterative ◽  
Periodic Boundary Value Problems ◽  
Functional Argument ◽  
First Order Differential Equations

Abstract This paper is concerned with periodic boundary value problems involving first order differential equations with functional arguments. The main feature of the paper is that the existence of maximal and minimal solutions is obtained by constructing sequences of upper and lower solutions of the initial value problems and not by establishing the comparison principle.

scholarly journals Periodic Boundary Value Problems for Semilinear Fractional Differential Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
Jia Mu ◽  
Yongxiang Li
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Periodic Boundary ◽  
Mild Solutions ◽  
Boundary Value ◽  
Upper And Lower Solutions ◽  
Parabolic Partial Differential Equations ◽  
Monotone Iterative ◽  
Periodic Boundary Value Problems ◽  
Fractional Differential

We study the periodic boundary value problem for semilinear fractional differential equations in an ordered Banach space. The method of upper and lower solutions is then extended. The results on the existence of minimal and maximal mild solutions are obtained by using the characteristics of positive operators semigroup and the monotone iterative scheme. The results are illustrated by means of a fractional parabolic partial differential equations.

scholarly journals Nonlinear boundary value problems for first order impulsive integro-differential equations

1989 ◽  
Vol 2 (3) ◽  
pp. 185-198 ◽  
Author(s):  
Xinzhi Liu
Keyword(s):  
Differential Equations ◽  
Boundary Value Problems ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Upper And Lower Solutions ◽  
Nonlinear Boundary Conditions ◽  
Nonlinear Boundary Value Problems ◽  
First Order ◽  
Monotone Iterative ◽  
Periodic Boundary Value Problems

In this paper, we investigate a class of first order impulsive integro-differential equations subject to certain nonlinear boundary conditions and prove, with the help of upper and lower solutions, that the problem has a solution lying between the upper and lower solutions. We also develop monotone iterative technique and show the existence of multiple solutions of a class of periodic boundary value problems.

scholarly journals Periodic Boundary Value Problems for First-Order Impulsive Functional Integrodifferential Equations with Integral-Jump Conditions

2014 ◽  
Vol 2014 ◽  
pp. 1-12
Author(s):  
Chatthai Thaiprayoon ◽  
Decha Samana ◽  
Jessada Tariboon
Keyword(s):  
Boundary Value Problems ◽  
Periodic Boundary ◽  
Boundary Value ◽  
Integrodifferential Equations ◽  
Jump Conditions ◽  
Comparison Result ◽  
First Order ◽  
Monotone Iterative ◽  
Periodic Boundary Value Problems ◽  
Minimal And Maximal Solutions

By developing a new comparison result and using the monotone iterative technique, we are able to obtain existence of minimal and maximal solutions of periodic boundary value problems for first-order impulsive functional integrodifferential equations with integral-jump conditions. An example is also given to illustrate our results.

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