scholarly journals Smooth Solutions of an Iterative Functional Differential Equation

2012 ◽  
Vol 02 (03) ◽  
pp. 138-143
Author(s):  
侯宇 赵
Keyword(s):  
Differential Equation ◽  
Functional Differential Equation ◽  
Smooth Solutions ◽  
Functional Differential ◽  
Iterative Functional Differential Equation

Smooth solutions of a nonhomogeneous iterative functional differential equation

1998 ◽  
Vol 128 (4) ◽  
pp. 821-831 ◽  
Author(s):  
Jian-Guo Si ◽  
Sui Sun Cheng
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Functional Differential Equation ◽  
Local Existence ◽  
Smooth Solutions ◽  
Local Existence Theorem ◽  
Forcing Function ◽  
Functional Differential ◽  
Iterative Functional Differential Equation

This paper is concerned with an iterative functional differential equation x(t) = c1x(t) + c2x[2](t) + … cmχ[m](t) + F(t), where x[i](t) is the i-th iterate of the function x(t). By means of Schauder's Fixed Point Theorem, we establish a local existence theorem for smooth solutions which also depend continuously on the forcing function F(t).

scholarly journals Smooth Solutions of a Class of Iterative Functional Differential Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-13
Author(s):  
Houyu Zhao
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Differential Equations ◽  
Functional Differential Equation ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Functional Differential Equations ◽  
Smooth Solutions ◽  
Functional Differential ◽  
Iterative Functional Differential Equation

By Faà di Bruno’s formula, using the fixed-point theorems of Schauder and Banach, we study the existence and uniqueness of smooth solutions of an iterative functional differential equationx′(t)=1/(c0x[0](t)+c1x[1](t)+⋯+cmx[m](t)).

scholarly journals Analytic Solutions of an Iterative Functional Differential Equation near Resonance

2009 ◽  
Vol 2009 ◽  
pp. 1-14 ◽  
Author(s):  
Tongbo Liu ◽  
Hong Li
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Functional Differential Equation ◽  
Unknown Function ◽  
Analytic Solutions ◽  
Complex Field ◽  
Second Order Differential Equations ◽  
Near Resonance ◽  
Functional Differential ◽  
Iterative Functional Differential Equation

We investigate the existence of analytic solutions of a class of second-order differential equations involving iterates of the unknown function in the complex field . By reducing the equation with the Schröder transformation to the another functional differential equation without iteration of the unknown function + = , we get its local invertible analytic solutions.

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