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.
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...
Z. Kamont, S. Kozieł (2006)
Annales Polonici Mathematici
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Classical solutions of functional partial differential inequalities with initial boundary conditions are estimated by maximal solutions of suitable problems for ordinary functional differential equations. Uniqueness of solutions and continuous dependence on given functions are obtained as applications of the comparison result. A theorem on weak functional differential inequalities generated by mixed problems is proved. Our method is based on an axiomatic approach to equations with unbounded...
J. Džurina (1997)
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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Our aim in this paper is to present the relationship between property (B) of the third order equation with delay argument y'''(t) - q(t)y(τ(t)) = 0 and the oscillation of the second order delay equation of the form y''(t) + p(t)y(τ(t)) = 0.