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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Wiley
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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| _version_ | 1832549490648678400 |
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| author | Houyu Zhao |
| author_facet | Houyu Zhao |
| author_sort | Houyu Zhao |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-152ba7c15d5044388956abd651d76b67 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-152ba7c15d5044388956abd651d76b672025-02-03T06:11:11ZengWileyAbstract 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 |
| spellingShingle | Houyu Zhao Analytic Solutions for a Functional Differential Equation Related to a Traffic Flow Model Abstract and Applied Analysis |
| title | 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_short | 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 |
| url | http://dx.doi.org/10.1155/2012/180595 |
| work_keys_str_mv | AT houyuzhao analyticsolutionsforafunctionaldifferentialequationrelatedtoatrafficflowmodel |