By defined holomorphic n-times integrated mild C-existence families and Csemigroups, their relationship with holomorphic mild C1-exustence families and holomorphic C1 -semigroups is discussed, respectively. For expone...By defined holomorphic n-times integrated mild C-existence families and Csemigroups, their relationship with holomorphic mild C1-exustence families and holomorphic C1 -semigroups is discussed, respectively. For exponentially bounded cases, this papergives several Hille-Yosida type conditions for an operator to have (or generate) one of thesefamilies of operators and generalize the corresponding results in [1], [2] and [3]. These families by the holomorphic solvability of the abstract Cauchy problem is also characterized.展开更多
In this paper, α -times integrated C-regularized cosine functions and mild α-times integrated C-existence families of second order are introduced. Equivalences are proved among α -times integrated C-regularized cos...In this paper, α -times integrated C-regularized cosine functions and mild α-times integrated C-existence families of second order are introduced. Equivalences are proved among α -times integrated C-regularized cosine function for a linear operator A, C-wellposed of (α + 1)-times abstract Cauchy problem and mild α -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 α -times integrated C-regularized cosine finction.The characterization of an exponentially botnded mild α -times integrated C-existence family of second order is given out in terms of a Laplace transform.展开更多
文摘By defined holomorphic n-times integrated mild C-existence families and Csemigroups, their relationship with holomorphic mild C1-exustence families and holomorphic C1 -semigroups is discussed, respectively. For exponentially bounded cases, this papergives several Hille-Yosida type conditions for an operator to have (or generate) one of thesefamilies of operators and generalize the corresponding results in [1], [2] and [3]. These families by the holomorphic solvability of the abstract Cauchy problem is also characterized.
基金This project is supported by the Natural Science Foundation of China and Science Development Foundation of the Colleges and University of Shanghai.
文摘In this paper, α -times integrated C-regularized cosine functions and mild α-times integrated C-existence families of second order are introduced. Equivalences are proved among α -times integrated C-regularized cosine function for a linear operator A, C-wellposed of (α + 1)-times abstract Cauchy problem and mild α -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 α -times integrated C-regularized cosine finction.The characterization of an exponentially botnded mild α -times integrated C-existence family of second order is given out in terms of a Laplace transform.
