Perturbations of existence families for abstract Cauchy problems

Xiao, Ti-Jun; Liang, Jin

doi:10.1090/S0002-9939-02-06627-3

Perturbations of existence families for abstract Cauchy problems
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Proc. Amer. Math. Soc. 130 (2002), 2275-2285 Request permission

Abstract:

In this paper, we establish Desch-Schappacher type multiplicative and additive perturbation theorems for existence families for arbitrary order abstract Cauchy problems in a Banach space: $u^{(n)}(t)=Au(t)$ $(t\geq 0)$; $u^{(j)}(0)=x_j\ (0\leq j\leq n-1)$. As a consequence, we obtain such perturbation results for regularized semigroups and regularized cosine operator functions. An example is also given to illustrate possible applications.

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