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International Journal of Mathematics and Mathematical Sciences
Volume 26 (2001), Issue 1, Pages 45-54

On nonautonomous second-order differential equations on Banach space

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

Received 7 June 1999

Copyright © 2001 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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), 0tT; u(0)=x0, u(0)=x1 on a Banach space by means of operator matrix method and apply to Volterra integrodifferential equations.