scholarly journals Analytic Solutions for a Functional Differential Equation Related to a Traffic Flow Model

2012 ◽  
Vol 2012 ◽  
pp. 1-13
Author(s):  
Houyu Zhao
Keyword(s):  
Differential Equation ◽  
Traffic Flow ◽  
Functional Differential Equation ◽  
Flow Model ◽  
Analytic Solutions ◽  
Auxiliary Equation ◽  
Traffic Flow Model ◽  
Near Resonance ◽  
Brjuno Condition ◽  
Functional Differential

We study the existence of analytic solutions of a functional differential equation(z(s)+α)2z'(s)=β(z(s+z(s))-z(s))which comes from traffic flow model. By reducing the equation with the Schröder transformation to an auxiliary equation, the author discusses not only that the constantλat resonance, that is, at a root of the unity, but also thoseλnear resonance under the Brjuno condition.

Analytic Solutions of a Nonhomogeneous Iterative Functional Differential Equation

2011 ◽  
Vol 474-476 ◽  
pp. 2155-2160
Author(s):  
Ling Xia Liu
Keyword(s):  
Differential Equation ◽  
Functional Differential Equation ◽  
Analytic Solutions ◽  
Diophantine Condition ◽  
Auxiliary Equation ◽  
State Dependent ◽  
Near Resonance ◽  
Brjuno Condition ◽  
Functional Differential ◽  
Iterative Functional Differential Equation

This paper is concerned with an iterative functional differential equation with state-dependent delay As well as in previous works, we reduce this problem with the Schroeder transformation to obtain auxiliary equation. For technical reasons, in previous work the constantgiven in the Schroeder transformation, is required to fulfill that is off the unit circle or lies on the circle with the Diophantine condition. In this paper, we discuss not only thoseat a root of the unity, but also those near resonance under the Brjuno condition.

Analytic Solutions of an Iterative Functional Differential Equation

2011 ◽  
Vol 474-476 ◽  
pp. 2208-2212
Author(s):  
Ling Xia Liu
Keyword(s):  
Differential Equation ◽  
Functional Differential Equation ◽  
Series Solution ◽  
Analytic Solutions ◽  
Diophantine Condition ◽  
Power Series Solution ◽  
Auxiliary Equation ◽  
Near Resonance ◽  
Functional Differential ◽  
Iterative Functional Differential Equation

This paper is concerned with the existence of analytic solutions of an iterative functional differential equation. By constructing a convergent power series solution of an auxiliary equation, analytic solutions for the original differential equation are obtained. We discuss not only those α at the hyperbolic case 0<|α|<1 but also those α near resonance under Diophantine condition.

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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