A parabolic differential equation with unbounded piecewise constant delay.
Wiener, Joseph, Debnath, Lokenath (1992)
International Journal of Mathematics and Mathematical Sciences
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Wiener, Joseph, Debnath, Lokenath (1992)
International Journal of Mathematics and Mathematical Sciences
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Wiener, Joseph, Debnath, Lokenath (1995)
International Journal of Mathematics and Mathematical Sciences
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Wiener, Joseph, Debnath, Lokenath (1997)
International Journal of Mathematics and Mathematical Sciences
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Villanueva, R.J., Hervas, A., Ferrer, M.V. (1995)
International Journal of Mathematics and Mathematical Sciences
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Alexander Rezounenko (2014)
Open Mathematics
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Systems of differential equations with state-dependent delay are considered. The delay dynamically depends on the state, i.e. is governed by an additional differential equation. By applying the time transformations we arrive to constant delay systems and compare the asymptotic properties of the original and transformed systems.
Kharatishvili, G., Tadumadze, T., Gorgodze, N. (2000)
Memoirs on Differential Equations and Mathematical Physics
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Papaschinopoulos, Garyfalos (1994)
International Journal of Mathematics and Mathematical Sciences
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Gil', M.I. (1998)
Journal of Inequalities and Applications [electronic only]
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Sokhadze, Z. (1995)
Memoirs on Differential Equations and Mathematical Physics
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Razzaghi, M., Marzban, H.R. (2001)
Mathematical Problems in Engineering
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Wiener, Joseph, Debnath, Lokenath (1992)
International Journal of Mathematics and Mathematical Sciences
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Yu, J.S., Chen, Ming-Po (1994)
International Journal of Mathematics and Mathematical Sciences
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Mihály Pituk, John Ioannis Stavroulakis (2025)
Czechoslovak Mathematical Journal
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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.