Semigroups of operators and abstract dynamic equations on time scales

Alaa E. Hamza and Karima M. Oraby

Applied Mathematics and Computation, 2015, vol. 270, issue C, 334-348

Abstract: In this paper we develop the theory of strongly continuous semigroups (C0-semigroups) of bounded linear operators from a Banach space X into itself. Many properties of a C0-semigroup {T(t):t∈T} and its generator A are established. Here T⊆R≥0 is a time scale endowed with an additive semigroup structure. We also establish necessary and sufficient conditions for the dynamic initial value problem {xΔ(t)=Ax(t),t∈Tx(0)=x0∈D(A),0∈Tto have a unique solution, where D(A) is the domain of A. Finally, we unify the continuous Hille–Yosida–Phillips Theorem and the discrete Gibson Theorem.

Keywords: Semigroups of operators; Generators and dynamic equations on Time scales (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:270:y:2015:i:c:p:334-348

DOI: 10.1016/j.amc.2015.07.110

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