| α-times Integrated Regularized Cosine Functions and Second Order Abstract Cauchy Problems |
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| 作者姓名： | 张寄洲 陶有山 |
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| 作者单位： | Zhang JizhouCollege of Mathematics Science，Shanghai Normal University，Shanghai，200234Tao YoushanDepartment of Applied Mathematics，Dong Hua University，Shanghai，200051 |
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| 基金项目： | This project is supported by the Natural Science Foundation of China and Science Development Foundation of the Colleges and University of Shanghai. |
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| 摘 要： | In this paper, a -times integrated C-regularized cosine functions and mild a -times integrated C-existence families of second order are introduced. Equivalences are proved among a -times integrated C-regularized cosine function for a linear operator A, C-wellposed of (a + l)-times abstract Cauchy problem and mild a -times integrated C-existence family of second order for A when the commutable condition is satisfied. In addition, if A = C~1AC, they are also equivalent to A generating the a -times integrated C-regularized cosine function. The characterization of an exponentially bounded mild a -times integrated C-existence family of second order is given out in terms of a Laplace transform.
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