On nonautonomous second-order differential equations on Banach space

International Journal of Mathematics and Mathematical Sciences（2001）

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Abstract

We show the existence and uniqueness of classical solutions of the nonau- tonomous 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.

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Key words

banach space,differential equations,second-order

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