On the Solution of the Cauchy Problem for a Second-Order Linear Differential Equation with Constant Unbounded Operator Coefficients in a Banach Space

摘要

In a Banach space E, we consider the Cauchy problem u"(t) + Bu'(t) + Cu(t) = f(t), 0 < t < ∞, (1) "(0) - u0, u'(0) = u'o, (2) with f(t) C([0,∞);E) and B,C N(E), where N(E) is the set of closed unbounded linear operators from E to E with dense domain in E.