On α-times integrated C-cosine functions and abstract Cauchy problem I

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:313

Article

Kuo, CC

关键词: alpha-times integrated C-cosine function;    generator;    abstract Cauchy problem;   

DOI  :  10.1016/j.jmaa.2005.06.089

来源: Elsevier

【 摘 要 】

In this paper we first investigate some basic properties concerning nondegenerate alpha-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) =Au(t)+f(t) fort >0, u(0)=x, u'(0)=y. (c) 2005 Elsevier Inc. All rights reserved.

【 授权许可】

Free