On nonautonomous second-order differential equations on Banach space

Abstract

We show the existence and uniqueness of classical solutions of the nonautonomous second-order equation: u″(t)=A(t)u′(t)+B(t)u(t)+f(t), 0≤t≤T; u(0)=x0, u′(0)=x1 on a Banach space by means of operator matrix method and apply to Volterra integrodifferential equations.