Regularized cosine existence and uniqueness families for second order abstract Cauchy problems
Volume 152 / 2002
Studia Mathematica 152 (2002), 131-145
MSC: Primary 47D06, 47D09; Secondary 34G10.
DOI: 10.4064/sm152-2-3
Abstract
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.
