Extension and Behavior at Infinity of Solutions of Certain Linear Operational Differential Equations

摘要

Let E be a complex Banach space, A, B linear operators with domains D(A), D(B) dense in E and range in E. An E-valued function u(.) defined and twice continuously differentiable in t = or > O is said to be a solution of the operational differential equation (1.1) u double prime + Bu(t) + Au(t) = O in (O, infinity) if u(t) epsilon D(A), u'(t) epsilon D(B), Au(.) and Bu(.) are continuous functions and (1.1) is satisfied everywhere in t = or > O. The problem of obtaining global estimates for the solutions of (1.1) are discussed on the basis of the given hypotheses. (Author)