Displaying similar documents to “Hamilton-Jacobi functional differential equations with unbounded delay”

Functional differential inequalities with unbounded delay

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...

Resolvent of nonautonomous linear delay functional differential equations

Joël Blot, Mamadou I. Koné (2015)

Nonautonomous Dynamical Systems

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The aim of this paper is to give a complete proof of the formula for the resolvent of a nonautonomous linear delay functional differential equations given in the book of Hale and Verduyn Lunel [9] under the assumption alone of the continuity of the right-hand side with respect to the time,when the notion of solution is a differentiable function at each point, which satisfies the equation at each point, and when the initial value is a continuous function.

An abstract Cauchy problem for higher order functional differential inclusions with infinite delay

Tran Dinh Ke, Valeri Obukhovskii, Ngai-Ching Wong, Jen-Chih Yao (2011)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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The existence results for an abstract Cauchy problem involving a higher order differential inclusion with infinite delay in a Banach space are obtained. We use the concept of the existence family to express the mild solutions and impose the suitable conditions on the nonlinearity via the measure of noncompactness in order to apply the theory of condensing multimaps for the demonstration of our results. An application to some classes of partial differential equations is given. ...

Characterization of shadowing for linear autonomous delay differential equations

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.

A Lyapunov functional for a system with a time-varying delay

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.