Analytic Solutions for a Functional Differential Equation Related to a Traffic Flow Model
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 constant λ at reson...
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| Format: | Article |
| Language: | English |
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Hindawi Limited
2012-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/180595 |
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doaj-152ba7c15d5044388956abd651d76b672020-11-24T23:25:19ZengHindawi LimitedAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/180595180595Analytic Solutions for a Functional Differential Equation Related to a Traffic Flow ModelHouyu Zhao0School of Mathematics, Chongqing Normal University, Chongqing 401331, ChinaWe 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 constant λ at resonance, that is, at a root of the unity, but also those λ near resonance under the Brjuno condition.http://dx.doi.org/10.1155/2012/180595 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Houyu Zhao |
| spellingShingle |
Houyu Zhao Analytic Solutions for a Functional Differential Equation Related to a Traffic Flow Model Abstract and Applied Analysis |
| author_facet |
Houyu Zhao |
| author_sort |
Houyu Zhao |
| title |
Analytic Solutions for a Functional Differential Equation Related to a Traffic Flow Model |
| title_short |
Analytic Solutions for a Functional Differential Equation Related to a Traffic Flow Model |
| title_full |
Analytic Solutions for a Functional Differential Equation Related to a Traffic Flow Model |
| title_fullStr |
Analytic Solutions for a Functional Differential Equation Related to a Traffic Flow Model |
| title_full_unstemmed |
Analytic Solutions for a Functional Differential Equation Related to a Traffic Flow Model |
| title_sort |
analytic solutions for a functional differential equation related to a traffic flow model |
| publisher |
Hindawi Limited |
| series |
Abstract and Applied Analysis |
| issn |
1085-3375 1687-0409 |
| publishDate |
2012-01-01 |
| description |
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 constant λ at resonance, that is, at a root of the unity, but also those λ near resonance under the Brjuno condition. |
| url |
http://dx.doi.org/10.1155/2012/180595 |
| work_keys_str_mv |
AT houyuzhao analyticsolutionsforafunctionaldifferentialequationrelatedtoatrafficflowmodel |
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1725558168669388800 |