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

Michael Gil’ ()
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Michael Gil’: Ben Gurion University of the Negev, Department of Mathematics

A chapter in Functional Equations and Ulam’s Problem, 2026, pp 127-150 from Springer

Abstract: 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.

Keywords: Banach space; Linear functional-differential equations; Exponential stability; Input-output stability; 34K30; 34K20; 34K06 (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-032-08949-6_7

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DOI: 10.1007/978-3-032-08949-6_7

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