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Modulus semigroups and perturbation classes for linear delay equations in L_p

By Hendrik Vogt and Jürgen Voigt


In this paper we study C0-semigroups on X×Lp(−h, 0; X) associated with linear differential equations with delay, where X is a Banach space. In the case that X is a Banach lattice with order continuous norm, we describe the associated modulus semigroup, under minimal assumptions on the delay operator. Moreover, we present a new class of delay operators for which the delay equation is well-posed for p in a subinterval of [1, ∞)

Topics: functional differential equation, delay equation, modulus semigroup, perturbation theory, domination
Year: 2009
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