### 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 (1992)

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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Wiener, Joseph, Debnath, Lokenath (1991)

International Journal of Mathematics and Mathematical Sciences

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Wiener, Joseph (1991)

International Journal of Mathematics and Mathematical Sciences

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Baštinec, Jaromír, Diblík, Josef (2004)

Abstract and Applied Analysis

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Gil', M.I. (1998)

Journal of Inequalities and Applications [electronic only]

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Papaschinopoulos, Garyfalos (1994)

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.

Győri, István, Pituk, Mihály (2001)

Journal of Inequalities and Applications [electronic only]

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Erik I. Verriest (2001)

Kybernetika

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A qualitative method is explored for analyzing the stability of systems. The approach is a generalization of the celebrated Lyapunov method. Whereas classically, the Lyapunov method is based on the simple comparison theorem, deriving suitable candidate Lyapunov functions remains mostly an art. As a result, in the realm of delay equations, such Lyapunov methods can be quite conservative. The generalization is here in using the comparison theorem directly with a different scalar equation...