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

Tom 152 / 2002

Jizhou Zhang Studia Mathematica 152 (2002), 131-145 MSC: Primary 47D06, 47D09; Secondary 34G10. DOI: 10.4064/sm152-2-3

Streszczenie

Let ${\bf C}_i$ $(i=1,2)$ be two arbitrary bounded operators on a Banach space. We study $({\bf C}_1, {\bf C}_2)$-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.

Autorzy

  • Jizhou ZhangDepartment of Mathematics
    Shanghai Normal University
    Shanghai 200234, People's Republic of China
    e-mail

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