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.

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.

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