Semigroups of operators and second-order Cauchy problems
Let A be the infinitesimal generator of a semigroup \(\{\) T(t)\(\}\) of operators in a Banach space X. Conditions are given which imply that \(u(t)=T(t)x\) is the only solution of the Cauchy problem \(u''(t)=A^ 2u(t),\quad u(0)=x\) that satisfies one of the conditions \(u(\infty -)=0\) or \(u(t)=O(1)\) at \(\infty\).
semigroup of operators in a Banach space
scientific article; zbMATH DE number 3888385