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Abstract
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International Journal of Mathematics and Mathematical Sciences 
Volume 26 (2001), Issue 1, Pages 45-54
doi:10.1155/S0161171201003519

On nonautonomous second-order differential equations on Banach space

Nguyen Thanh Lan

Department of Mathematics, Ohio University, Athens 45701, OH, USA

Received 7 June 1999

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.