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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

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.