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 Existence of triple positive periodic solutions of a functional differential equation depending on a parameter

2004 ◽  
Vol 2004 (10) ◽  
pp. 897-905 ◽  
Author(s):  
Xi-lan Liu ◽  
Guang Zhang ◽  
Sui Sun Cheng
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Periodic Solutions ◽  
Functional Differential Equation ◽  
Point Theorem ◽  
Functional Differential Equations ◽  
Positive Periodic Solutions ◽  
Functional Differential

We establish the existence of three positive periodic solutions for a class of delay functional differential equations depending on a parameter by the Leggett-Williams fixed point theorem.

scholarly journals On the Existence and Stability of Periodic Solutions for a Nonlinear Neutral Functional Differential Equation

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Yueding Yuan ◽  
Zhiming Guo
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Periodic Solutions ◽  
Functional Differential Equation ◽  
Point Theorem ◽  
Sufficient Conditions ◽  
Neutral Functional Differential Equation ◽  
Existence And Stability ◽  
Functional Differential

This paper deals with the existence and stability of periodic solutions for the following nonlinear neutral functional differential equation(d/dt)Dut=p(t)-au(t)-aqu(t-r)-h(u(t),u(t-r)).By using Schauder-fixed-point theorem and Krasnoselskii-fixed-point theorem, some sufficient conditions are obtained for the existence of asymptotic periodic solutions. Main results in this paper extend the related results due to Ding (2010) and Lopes (1976).

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