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Regularized cosine existence and uniqueness families for second order abstract Cauchy problems

Jizhou Zhang — 2002

Studia Mathematica

Let $C_{i}$ (i = 1,2) be two arbitrary bounded operators on a Banach space. We study (C₁,C₂)-regularized cosine existence and uniqueness families and their relationship to second order abstract Cauchy problems. We also prove some of their basic properties. In addition, Hille-Yosida type sufficient conditions are given for the exponentially bounded case.

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