A class of complete second order linear differential equations

Abstract:

This paper is concerned with a class of complete second order linear differential equations in a Banach space. We show the existence and uniqueness of classical solutions of \begin{equation}\tag {SE} \begin {cases} u''(t) = A(t)u’(t) + B(t)u(t) + f(t) \text {for $t \in [0,T]$} \ u(0) = x \text {and} u’(0) = y. \end{cases} \end{equation}