Abstract
In this paper, the existence of analytic solution of an iterative functional differential equation is studied. By reducing the equation with the Schröder transformation to the another functional equation with proportional delay, an existence theorem is established for analytic solutions of the original equation. For technical reasons, in previous work the constant β given in the Schröder transformation, is required to satisfy that β is off the unit circle S 1 or lies on the circle with the Diophantine condition. In this paper, we give results of analytic solutions in the case of β at resonance, i.e., at a root of the unity and β is near resonance under the Brjuno condition.
Supported by the Natural Science Foundation of Shandong Province (2006ZRB01066).
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Liu, L. (2010). The Exist Local Analytic Solutions of an Iterative Functional Differential Equation. In: Huang, DS., Zhang, X., Reyes García, C.A., Zhang, L. (eds) Advanced Intelligent Computing Theories and Applications. With Aspects of Artificial Intelligence. ICIC 2010. Lecture Notes in Computer Science(), vol 6216. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14932-0_3
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DOI: https://doi.org/10.1007/978-3-642-14932-0_3
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