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Stability Conditions for Linear Functional-Differential Equations in a Banach Space. A Brief Survey

In: Functional Equations and Ulam’s Problem

Author

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  • Michael Gil’

    (Ben Gurion University of the Negev, Department of Mathematics)

Abstract

This chapter is a brief survey of the recent results of the author devoted to the stability of linear functional-differential equations in a Banach space. We consider autonomous and non-autonomous equations with bounded and unbounded operators. The illustrative examples with partial differential and integro-differential equations are also presented. These examples show that the obtained stability conditions allow us to avoid in appropriate situations the construction of the Krasovskij-Lyapunov type functionals. In the case of unbounded operators we generalize the well-known Dyson-Phillips theorem on perturbations of strongly continuous semigroups to the fundamental solutions of differential-difference equations in a Banach space.

Suggested Citation

  • Michael Gil’, 2026. "Stability Conditions for Linear Functional-Differential Equations in a Banach Space. A Brief Survey," Springer Books, in: Themistocles M. Rassias (ed.), Functional Equations and Ulam’s Problem, pages 127-150, Springer.
    • Handle: RePEc:spr:sprchp:978-3-032-08949-6_7
    DOI: 10.1007/978-3-032-08949-6_7
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