Article
Full entry | Fulltext not available
(moving wall
24 months)
Feedback
Keywords:
delay differential equation; linear autonomous equation; shadowing
delay differential equation; linear autonomous equation; shadowing
Summary:
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.
References:
[1] Backes, L., Dragičević, D.: Shadowing for infinite dimensional dynamics and exponential trichotomies. Proc. R. Soc. Edinb., Sect. A, Math. 151 (2021), 863-884. DOI 10.1017/prm.2020.42 | MR 4259329 | Zbl 1470.37028
[2] Backes, L., Dragičević, D., Pituk, M., Singh, L.: Weighted shadowing for delay differential equations. Arch. Math. 119 (2022), 539-552. DOI 10.1007/s00013-022-01769-3 | MR 4496984 | Zbl 1515.34064
[3] Brzdęk, J., Popa, D., Raşa, I., Xu, B.: Ulam Stability of Operators. Mathematical Analysis and its Applications. Academic Press, London (2018). DOI 10.1016/c2015-0-06292-x | MR 3753562 | Zbl 1393.39001
[4] Buse, C., Saierli, O., Tabassum, A.: Spectral characterizations for Hyers-Ulam stability. Electron. J. Qual. Theory Differ. Equ. 2014 (2014), Article ID 30, 14 pages. DOI 10.14232/ejqtde.2014.1.30 | MR 3218777 | Zbl 1324.34022
[5] Hale, J. K., Lunel, S. M. Verduyn: Introduction to Functional Differential Equations. Applied Mathematical Sciences 99. Springer, New York (1993). DOI 10.1007/978-1-4612-4342-7 | MR 1243878 | Zbl 0787.34002
[6] Palmer, K.: Shadowing in Dynamical Systems: Theory and Applications. Mathematics and its Applications (Dordrecht) 501. Kluwer, Dordrecht (2000). DOI 10.1007/978-1-4757-3210-8 | MR 1885537 | Zbl 0997.37001
Search
Partner of
