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Analytic Solutions of an Iterative Functional Differential Equation with State Dependent Delay

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Software Engineering and Knowledge Engineering: Theory and Practice

Part of the book series: Advances in Intelligent and Soft Computing ((AINSC,volume 115))

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Abstract

This paper is concerned with a functional differential equation with state dependent delay. By constructing a convergent power series solution of an auxiliary equation, analytic solutions for the original differential equation are obtain. For technical reasons, in previous work the constant α given in the Schröder transformation, is required to fulfill that α is off the unit circle or lies on the circle with the Diophantine condition. In this paper, we obtain results of analytic solutions in the case of α at resonance, i.e., at a root of the unity and the case of α near resonance under the Brjuno condition.

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Authors and Affiliations

  1. Department of Mathematics, Weifang University, Weifang, Shandong, 261061, P. R. China

    Lingxia Liu

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  1. Lingxia Liu
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Correspondence to Lingxia Liu .

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Editors and Affiliations

  1. Central China Normal University, Lvting Yajing, Hongshan Qu 10-3-102, Wuhan, 430079, China, People's Republic

    Yanwen Wu

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Liu, L. (2012). Analytic Solutions of an Iterative Functional Differential Equation with State Dependent Delay. In: Wu, Y. (eds) Software Engineering and Knowledge Engineering: Theory and Practice. Advances in Intelligent and Soft Computing, vol 115. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25349-2_2

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  • DOI: https://doi.org/10.1007/978-3-642-25349-2_2

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-25348-5

  • Online ISBN: 978-3-642-25349-2

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