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Analytic Solutions of a Second-Order Iterative Functional Differential Equations

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Advanced Research on Electronic Commerce, Web Application, and Communication (ECWAC 2011)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 143))

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Abstract

In this paper, the existence of analytic solutions of an iterative functional differential equation is studied. We reduce this problem to finding analytic solutions of a functional differential equation without iteration of the unknown function. For technical reasons, in previous work the constant α given in 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 break the restraint of the Diophantine condition and 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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Author information

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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Editors and Affiliations

  1. Wuhan University of Science and Technology, Zhongnan Branch, No.18, Jiangxia Road, Wuhan, China

    Gang Shen  & Xiong Huang  & 

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Liu, L. (2011). Analytic Solutions of a Second-Order Iterative Functional Differential Equations. In: Shen, G., Huang, X. (eds) Advanced Research on Electronic Commerce, Web Application, and Communication. ECWAC 2011. Communications in Computer and Information Science, vol 143. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20367-1_44

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  • DOI: https://doi.org/10.1007/978-3-642-20367-1_44

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-20366-4

  • Online ISBN: 978-3-642-20367-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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