Spectrum of A Class of Delay Differential Equations and Its Solution Expansion
نویسنده
چکیده
Abstract: In this paper we study the spectrum and solution expansion of the differential equation with multiple delays. Firstly, we present explicitly the asymptotic expressions of the eigenvalues under certain conditions. Then we prove that the root vectors of the system fail to form a basis for the state Hilbert space. However, by a trick, we expand the solution of the system according to the root vectors. As an application, we explain how to apply solution expansion to the numerical simulation of this kind of delay differential equations.
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تاریخ انتشار 2011