Abstract
A well-known shadowing theorem for ordinary differential equations is generalized to delay differential equations. It is shown that a linear autonomous delay differential equation is shadowable if and only if its characteristic equation has no root on the imaginary axis. The proof is based on the decomposition theory of linear delay differential equations.
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Dedicated to the memory of Professor Jaroslav Kurzweil
M. Pituk was supported in part by the Hungarian National Research, Development and Innovation Office Grant No. K139346. J. I. Stavroulakis was supported by the Thesis scholarship of Ariel University. Open access funding provided by University of Pannonia.
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Pituk, M., Stavroulakis, J.I. Characterization of shadowing for linear autonomous delay differential equations. Czech Math J (2024). https://doi.org/10.21136/CMJ.2024.0191-23
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DOI: https://doi.org/10.21136/CMJ.2024.0191-23