Zdeněk Svoboda, Faculty of Electrical Engineering and Communication, Brno University of Technology, Brno, Czech Republic, e-mail: svobodaz@feec.vutbr.cz
Abstract: We study the asymptotic behavior of the solutions of a differential equation with unbounded delay. The results presented are based on the first Lyapunov method, which is often used to construct solutions of ordinary differential equations in the form of power series. This technique cannot be applied to delayed equations and hence we express the solution as an asymptotic expansion. The existence of a solution is proved by the retract method.
Keywords: asymptotic expansion, retract method
Classification (MSC 2010): 34E05
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