Abstract
In this paper we first investigate some basic properties concerning nondegenerate α-times integrated C-cosine functions on a Banach space X, and then characterize their generator A in terms of the unique existence of strong solutions of the following abstract Cauchy problem: ACP ( f , x , y ) u ″ ( t ) = A u ( t ) + f ( t ) for t > 0 , u ( 0 ) = x , u ′ ( 0 ) = y .
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