Abstract
In this paper, we study a class of semilinear systems with state and input delays. We prove that the well-posedness of the considered delay systems, the associated semilinear systems without delays, and the associated extended abstract Cauchy problems are equivalent in the sense of strong solutions. Moreover, some existence conditions of strong solutions of the considered delay systems are deduced. As an application, a nonlinear population dynamics problem with delays in state and input is presented.
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This work was supported by the Natural Science Foundation of China (project No. 60970149).
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Mei, ZD., Peng, JG. & Song, XL. A class of semilinear systems with state and input delays. J Dyn Control Syst 17, 123–139 (2011). https://doi.org/10.1007/s10883-011-9112-5
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DOI: https://doi.org/10.1007/s10883-011-9112-5