Mouffak Benchohra, Imene Medjadj (2016)
Commentationes Mathematicae Universitatis Carolinae
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Our aim in this work is to provide sufficient conditions for the existence of global solutions of second order neutral functional differential equation with state-dependent delay. We use the semigroup theory and Schauder's fixed point theorem.
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.
Józef Duda (2010)
Control and Cybernetics
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Józef Duda (2010)
Control and Cybernetics
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Gil', M.I. (2009)
Electronic Journal of Qualitative Theory of Differential Equations [electronic only]
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Abdessalam Baliki, Mouffak Benchohra (2014)
Nonautonomous Dynamical Systems
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In this paper we prove the global existence and attractivity of mild solutions for neutral semilinear evolution equations with state-dependent delay in a Banach space.
Sokhadze, Z. (1995)
Memoirs on Differential Equations and Mathematical Physics
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Józef Duda (2012)
International Journal of Applied Mathematics and Computer Science
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The paper presents a method to determine a Lyapunov functional for a linear time-invariant system with an interval timevarying delay. The functional is constructed for the system with a time-varying delay with a given time derivative, which is calculated on the system trajectory. The presented method gives analytical formulas for the coefficients of the Lyapunov functional.
Sonnenberg, Amnon, Crain, Bradford R. (2005)
Journal of Theoretical Medicine
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A. F. Ivanov (1989)
Banach Center Publications
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James Louisell (2001)
Kybernetika
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In this paper we give an example of Markus–Yamabe instability in a constant coefficient delay differential equation with time-varying delay. For all values of the range of the delay function, the characteristic function of the associated autonomous delay equation is exponentially stable. Still, the fundamental solution of the time-varying system is unbounded. We also present a modified example having absolutely continuous delay function, easily calculating the average variation of the...