Analytic Solutions of a Nonhomogeneous Iterative Functional Differential Equation

Ling Xia Liu

doi:10.4028/www.scientific.net/KEM.474-476.2155

Paper Titles

Effect of Nanocrystalline and Ti Implantation on the Oxidation Behaviour of Fe₈₀Cr₂₀Alloy and Commercial Ferritic Steel
p.2134

The Study of Forest Fire Color Image Segmentation
p.2140

The 3-D Simulation of the LNGC in Pre-Cooling Process
p.2146

Based on RFID Food Supply Chain Traceability System Framework Design
p.2150

Analytic Solutions of a Nonhomogeneous Iterative Functional Differential Equation
p.2155

Research on Impact of Radio Irregularity on Self-Localization of WSN
p.2161

Informationization Modes Study for Discrete Manufacturing Enterprises in China
p.2167

A High Throughput GALS Wrapper with Virtual Channels
p.2171

Development and Application of Driving Devices for Space Environment
p.2177

HomeKey Engineering MaterialsKey Engineering Materials Vols. 474-476Analytic Solutions of a Nonhomogeneous Iterative...

Analytic Solutions of a Nonhomogeneous Iterative Functional Differential Equation

Abstract:

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.

You might also be interested in these eBooks

View Preview

Info:

Periodical:

Key Engineering Materials (Volumes 474-476)

Pages:

2155-2160

DOI:

https://doi.org/10.4028/www.scientific.net/KEM.474-476.2155

Citation:

Cite this paper

Online since:

April 2011

Authors:

Ling Xia Liu

Keywords:

Analytic Solution, Brjuno Condition, Iterative Functional Differential Equation, Resonance, Schroeder Transformation

Export:

RIS, BibTeX

Price:

Permissions CCC:

Request Permissions

Permissions PLS:

Request Permissions

Сopyright:

Citation:

References

[1] E. Eder: The functional differential equation . J. Differential Equa., Vol. 54, pp.390-400 (1984).

Google Scholar

[2] Z. Jackiewicz: Existence and uniqueness of solutions of neutral delay-differential equations with state dependent delays. Funkcial Ekvac., Vol. 30, pp.9-17 (1987).

Google Scholar

[3] J.G. Si, W.R. Li, and S.S. Cheng: Analytic solutions of an iterative functional differential equation. Computer Math. Applic, vol. 33, no. 6, pp.47-51(1997).

Google Scholar

[4] J.G. Si, S.S. Cheng: Note on an iterative functional differential equations. Demonstratio Math., vol. 31, no. 3, pp.609-614(1998).

Google Scholar

[5] J.G. Si and S.S. Cheng: Smooth solutions of a nonhomogeneous iterative functional differential equations. Proc. Royal Soc. Edinburgh(A), vol. 128, pp.821-831(1998).

DOI: 10.1017/s0308210500021806

Google Scholar

[6] A. D. Bjuno: Analytic form of differential equations. Trans. Moscow Math. Soc., vol. 25, pp.131-288 (1971).

Google Scholar

[7] S. Marmi, P. Moussa and J.C. Yoccoz: The Brjuno functions and their regularity properties. Comm. Math. Phys., vol. 186, no. 2, pp.265-293(1997).

DOI: 10.1007/s002200050110

Google Scholar

[8] T. Carletti and S. Marmi: Linearization of Analytic and Non-Analytic Germs of Diffeomorphisms of C Bull. Soc. Math., France, vol. 128, pp.69-85 (2000).

DOI: 10.24033/bsmf.2363

Google Scholar

[9] A. M. Davie: The critical function for the semistandard map. Nonlinearity, vol. 7, pp.219-229, (1994).

DOI: 10.1088/0951-7715/7/1/009

Google Scholar